Astrophysical significance of black holes

In the previous few chapters, we have built up the theory of black holes, which are (along with the global structure and evolution of the entire universe) the most extreme manifestation of the properties of gravity. It's time to turn to real nature and ask: Are there black holes in the universe? And what is the role do these black holes in universe?
Note:Only the "outer" part of the black hole above the event horizon has astrophysical significance for the processes taking place in space, not the "inner" asymptotically future area below the horizon (in connection with the dynamics of gravitational collapse it was discussed in §4.2, passage "There are "complete" black holes in space?").
Opinions on the role of black holes in space have changed radically in recent decades. Until the mid-1960s, astronomers did not take the possibility of gravitational collapse (the term "black hole" did not exist at that time) too seriously - they believed that all stars would lose enough mass during their evolution to avoid gravitational collapse (renowned English astronomer A.S.Eddington sought natural law or a mechanism that would "prevent the stars from doing such nonsenses"!). After the discovery of quasars - see note below *) and pulsars this position began to change rapidly. In the half of the 1970s, black holes became so popular, that astrophysicists used them to explain almost all new or as yet unexplained phenomena - not just X-ray sources, quasars and active galaxy nuclei, the mystery of missing matter in spiral galaxies and galaxy clusters etc., but also, for example, the lack of solar neutrinos, the fall of the Tunguska meteorite, or even the disappearance of ships in the Bermuda Triangle...
Later, when a some "sobering up" has occurred, probable hypotheses about the role of black holes in space have already separated from unrealistic fabrications (such as the last three mentioned above), which have shifted from the pages of professional treatises to the field of sci-fi literature. Black hole astrophysics now has relatively close contact with astronomical observations, so that black holes are given an increasingly objective and adequate place and role in space.

*) Quasars and radio galaxies
In 1960, a strange radio source 3C48 of very small angular size (less than 1 arcsecond) was observed with a Jodrell Bank radio telescope, which was identified in the optical field with a Palomar 5-meter telescope with a faint bluish point object that looked like a star. But the spectrum of this object was very strange, its lines were completely different from the radiation of any star. Over the next few years was discovered a number of these special objects "like the stars" - quasistelar objects in short called quasars (quasar - quasi-stellar object).
The spectra of quasar radiation at first seemed utterly mysterious. In the end, however, it was found that the strange spectra of these objects are still formed by standard spectral lines of hydrogen, oxygen, magnesium, ... etc., which are emitted by atoms of excited gas in ordinary stars (or on Earth), which, however, do not have their usual wavelengths, but they are significantly shifted to the red end of the spectrum (by tens of %). According to the Doppler effect, this means that these objects must move away from us at a speed close to the speed of light (for the first observed quasars it was about 16% - 40% c ).
Such tremendous speeds indicated that they could not be stars in our Galaxy, but that quasars were objects from distant space that are moving away from us due to the cosmological expansion of the universe. Since, according to Hubble's law (see §5.1), the velocity of the distance is directly proportional to the actual distance of the object, the distance of the first observed quasars was about 2-5 billion light-years.
This means, however, that in order for quasars to be as bright as the astronomically observed from such a vast distance, they must have a huge radiant power - about 100 times larger than the brightest galaxies! Furthermore, the brightness of quasars was found to be variable, changes significantly in time scales of about 1 month. However, this shows that most of the light from such a source must be emitted from space smaller than 1 "light moon", ie from an area about a million times smaller in diameter than galaxies. The radiation must therefore come from a very massive compact object made of hot gases, heated by an extremely powerful energy source. It turns out that such a "quasar engine" is probably a giant black hole in the core of the galaxy. As will be discussed below, a black hole can act as a "machine" that converts a portion of the mass of the surrounding absorbed gas into heat in a rotating accretion disk, which is then converted to radiation. Such a "gravitational aggregate" could be highly efficient, significantly more efficient than a fission nuclear and even a thermonuclear reactors!
Long before that, in fact, from the 1930s, when radio radiation from space began to be registered, some objects in distant space emitting radio waves were observed. Later, when the principle of radio interferometry of signals from a large number of distant antennas succeeded in significantly improving the angular resolution, so-called radio galaxies were discovered - large regions in the distant universe emitting radio waves. At first it seemed to be a collision of two galaxies, but further observations showed that it was the only galaxy from the center of which large clouds emanate, a kind of "lobes" emitting radio waves. A detailed atlas of such radiation-active galaxies compiled by K.Seyfert in the 1940s and therefore galaxies with active nuclei are sometimes referred to as Seyfert galaxies.
Near the source nuclei of galaxies, these radio-emitting clouds have the shape of narrowly collimated jets of very fast particles, which are only braked at great distances in the intergalactic environment, where they end in large radio lobes reaching distances of several parsecs to hundreds of kiloparsecs - Fig.4.29. The observed geometry of the jets from the active nuclei of galaxies suggests that the particle beams emitted from the compact source in the galaxy nucleus have a very stable geometric axis, the direction of which has remained virtually unchanged for about 10⁶ -10⁸ years. The source of the jets must therefore be a very massive rotating structure, the angular momentum of which, with its gyroscopic effect, guarantees a spatially stable axis of rotation along which the jets point. Below we will see that there is a very close connection between the active nuclei of galaxies and quasars (+ blazars): the common essence is massive jets of radiation, particles and gas from rotating accretion disks around giant black holes in the center of galaxies, with gas and radiation flow tightly bound with the axis of rotation of the black hole. This is the same phenomenon, observed only from different angles (discussed below in the section "Mechanism of quasars and active nuclei of galaxies").
Blazars
Special types of highly luminous quasars with rapid changes in brightness, which greatly shine even in the ultraviolet, X-ray or gamma of the spectrum are called blazars (blazing quasi-stellar object - blazing, flaming quasar, the name derives also from the combination of the name of emission galaxy BL Lacertae and strongly variable quasars). They are some of the most energetic sources of radiation observed in the universe. The blazar effect is probably due to the observation of a quasar rotated by its rotational axis, ie the jet line (see "Thick accretion disks. Quasars" below), exactly in the direction of the observer, where clearer radiation is observed and the variability of radiation intensity is best seen.

Origin and Occurrence of Black Holes
Although, according to current astrophysics, there should be a large number of black holes occur in our galaxy (and a significant percentage of stars should end up as black holes), the existence of black holes has not been proven immediately and with absolute certainty for a long time. It is not surprising, because a black hole with the mass of an average star is an object with effective dimensions of the order of kilometers to tens of kilometers, which itself practically does not glow and is therefore not observable at large interstellar distances. We have a no chance to reveal a lone black hole traveling through empty space. Simply put, no one has ever seen black holes and will never see the future - noting from them can be seen, it's just a bizarre empty and dark place in space... We could see, at most, only the "silhouette" of a black hole (its horizon or photon sphere) against the background of brighter cosmic objects, or manifestations of a gravitational lens (§4.3, passage "Gravitational lenses. Optics of black holes.").
However, below we will describe some phenomena where we do not see the black hole itself, but its existence is pointed out by phenomena occurring in its immediate vicinity *) - a black hole can be inferred indirectly on the basis of significant manifestations of its interaction with the surrounding matter.
*) The black hole itself cannot be visually observed as it follows from its very essence - the presence of the event horizon. However, we can observe the manifestations of the effect of its massive gravitational field on the surrounding matter, or to transmitted light. E.g. when stars and gas orbit a massive invisible object, it is an indication for a black hole. And as we'll see below, the accretion disks around the massive black holes may even be the most intense sources of radiation in the universe!
First, we notice the situations in which black holes can be expected to form and the mechanisms by which black holes are formed.

Black holes of stellar masses
In §4.2 we showed the easiest way to produce black holes: a star with enough weight *) after consumption of nuclear "fuel" collapses nearly spherical, and if the remaining mass is large enough, neither the collapse of a white dwarf nor the neutron star will stop (no equilibrium configuration for such a large mass does not exist), an event horizon is formed and a black hole is created. In §4.4 (Fig.4.14) a somewhat more complicated case was mentioned, when the rapid rotation first led to fragmentation (thus delaying another collapse for some time) and only after the excess angular momentum was radiated by the gravitational waves, did the collapse and the formation of the resulting rotating black hole be completed. In this way, black holes of stellar masses M ~ (2÷100)M_¤ can form both alone and in multiple star systems.
*)The condition is that the mass after the end of thermonuclear reactions exceeds ~ 2M_¤ (Oppenheimer-Landau limit). According to today's knowledge about the evolution of stars, it is necessary for the initial mass of a star to exceed about ~10-20 M_¤; lighter stars end their existence mostly like neutron stars or white dwarfs (due to the large mass losses of stars during their long evolution).
In a close binary system, a black hole can be formed by an indirect mechanism, so that from one component (which is a giant star) it flows through the inner Lagrange point (see §1.2, Fig.1.1d , passage "Binary system") to the other component, which is a white dwarf or neutron star, a considerable amount of matter (the situation is similar to Fig.4.26). After a certain time, the Oppenheimer-Landau limit is reached by accretion, a complete collapse occurs and a black hole is formed. The flowing mass is then still absorbed by this black hole, around which an accretion disk forms, see below.
It is estimated that our Milky Way could contain ~100 million black holes formed at the end of the evolutionary path of massive stars.

Medium-sizes and giant black holes
Furthermore, black holes can form in a system of a large number of stars - in galactic nuclei or star clusters If the stars in such a system is too "crampedly", there will be inelastic interactions and collisions, which will lead to the merging of some stars into compact structures. They can be formed, and gradually increase very massive objects, that can easily become so thick that it collapses into a medium-sizes black holes from weights from ~10²-10⁴M_¤ (in star clusters), or into a giant black holes up to ~10⁹-10¹²M_¤ (at galaxies - see below "Mechanism of quasars and active nuclei of galaxies"). The whole process can take place in a very diverse way, eg it can be combined with the normal collapse of some of the participating stars and subsequent fusion of black holes and the like (the possibilities for the formation of supermassive black holes in the center of galaxies are briefly discussed below in the section "How did the central supermassive black holes form?").
The result of such processes may be the entire range of masses of black holes - from tens or hundreds of M_¤, over thousands or millions of M_¤, to the giant black hole weighing many billions M_¤ located probably in the center of large galaxies (see "Thick accretion discs. Quasars"). In terms of astronomical observations, there are already strong indications (see below) for black holes of stellar masses, and supermassive black holes in the cores of galaxies. The medium-mass black holes (~ 10²-10⁴ M_¤), expected in star clusters, have not yet been observed (certain indications for a black hole of mass ~5-8x10³M_¤ were observed in the center of the globular star cluster Omega Centauri).
Black holes in the center of galaxies
In the center of our Galaxy is observed the object Sagitarius A, around which the stars of the central star cluster in the Milky Way and gases orbit at such a high speed (approaching c/3), that a very massive object with a mass of about 4 millions of M_¤ must be in the center - supermassive black hole. Such black "giant-holes" probably occur in the center of all galaxies. Inside some galaxies, there may be even two large black holes, clogged there in the distant past in the collision and fusion of two galaxies (galactic "cannibalism"), which had previously formed their supermassive black holes at their centers; they then orbit large distances of tens or hundreds of light-years in the resulting galaxy.
From an astrophysical point of view, it can be expected that in the central regions of galaxies, where in dense gas clouds there are ideal conditions for the formation of massive stars, which soon collapse into black holes, hundreds or thousands of smaller black holes (weighing about tens of M_¤) may occur, some of which may orbit the central giant black hole. And astrophysical estimates suggest that up to 100 million black holes may occur throughout the Milky Way.
In some clusters, such as the globular cluster NGC 6624, a sharp maximum mass density at the center and strong X-ray emission have been observed, indirectly indicating for the presence of a large black hole. In the cores of many (maybe even most) of galaxies exist conditions for giant black holes to form, and galactic nuclei activity observation suggests that similarly processed are actually taking place there (see below, "The mechanism of active cores and quasar galaxies").

Left : Large black holes could be found inside globular clusters.		Right : Two massive jets flow from the radiation-active elliptical galaxy NGC 4261 (45 million light-years away).
Gigantic black holes could be found in the cores of galaxies.		At the core of this active galaxy, the Hubble Space Telescope has found a gas-dust disk about 400 light-years across, perpendicular to jets.
	On the possibilities of the existence of black holes in the center of star clusters and in the cores of galaxies.

Flashes of radiation during the formation of black holes
Such a high-energy and "catastrophic" phenomenon, such as the complete gravitational collapse and the formation of a black hole, is of course accompanied by significant "accompanying phenomena". In massive stars, which were born 20 or more times the mass of the Sun, a gravitational collapse occurs after the depletion of thermonuclear fuel - a supernova explosion in which the star's core collapses directly into a black hole, without the formation of a neutron star. In less massive stars, the product of a supernova explosion is a neutron star, which may later collapse into a black hole by accretion of material or fusion with another compact object in a binary or multiple system. An important side effect of these processes is the sudden release of a huge amount of energy - a rapidly expanding "fireball" is formed from the rapidly accelerated material surrounding the star. Shock waves often occur in the expanding material as the faster grouping strikes and precedes the slower grouping. The vast amount of radiation and energetic particles, emitted in the form of a massive flash during this explosion is probably an important source of cosmic radiation propagating through space. In the case of rapid rotation, the surrounding material has a disk shape and usually produces a very strong magnetic field. The expanding hot gas is then formed into a pair of jets along the rotational axis of the system.
Additional intense radiation is continuously generated during the accretion of the substance, as discussed below in the section "Accretion disks around black holes".

Primordial black holes ?
An interesting hypothesis is the black holes of primordial origin, which could have formed in large numbers from the hot, extremely dense plasma that filled the universe immediately after the Big Bang. Microscopic quantum fluctuations increase to a macroscopic scale as inflation expands - creating areas with significantly lower and higher densities of matter and energy, from which all structures in the universe later emerged ( §5.5 "Microphysics and Cosmology. Inflation Universe."). In the very early stages of the universe, soon after the inflationary period, a large amount of significant densities could be present, which could collapse locally into black holes. Such a large amount would be created primordial black holes of various weights.
In this way, primordial black holes of both high masses and (as opposed to gravitational collapse) of arbitrarily small masses could be formed; this mass would then decide their future. Large primordial black holes will enlarge due to the accretion of radiation and matter, so they could now grow into gigantic masses (perhaps up to 10¹⁵M_¤) of observed supermassive black holes in the center of galaxies (see below "Mechanism of quasars and active nuclei of galaxies"). For very small primordial black holes would in turn prevail quantum evaporation (see §4.7 "Quantum radiation and thermodynamics of black holes", section "Quantum radiation from black holes")); all primordial black holes weighing less than about 10¹⁵g would have to evaporate completely to this day *). The final phase of quantum evaporation will take place very quickly, it is explosive in nature and a large amount of energy will be released in the form of a flash of mainly hard gamma radiation and high-energy particles. For the existence of primordial black mini-holes are not yet any direct or indirect evidence (observation trying to register the appropriate hard gamma bursts were unsuccessful), so their astrophysical significance is mostly not reflected.
*) With the Hawking effect, in a vacuum every black hole of mass M evaporates completely in about T ~ 10⁶⁵. (M/M_¤)³ years.
Dark matter?
Smaller and medium primordial black holes (~10^-18÷10^-6M_¤), formed in the first second after the big bang, possibly in large quantities, would be stable in the long term and would also occur in the present universe. Sometimes they are considered as one of the suitable "candidates" for hidden - dark - matter in galaxies and clusters of galaxies (§5.6, passage "Future development of the universe. Hidden-dark matter."). This explanation would be quite convincing because it would not require looking for unknown particles outside the standard model. It is not known how many of them were created at the beginning of the universe, whether their number is sufficient to explain dark matter. Detecting these primordial black holes is difficult, perhaps using gravitational micro-lensing. This origin of dark matter has not yet been proven...
"Parasitic" black holes inside stars ?
There were even hypotheses (in the 1970s by S.Hawking) that "endoparasitic" primordial black holes could also reside in the interior of some stars and were "eating" them from the inside. The direct capture and absorption of a small black hole by an already "finished" star is unlikely. Due to the high speed and large impact parameter, they would mostly fly past the star without being captured. Even those black holes that would hit a star directly would mostly fly through its material without significant braking by friction or accretion and fly away; their speed is usually greater than the escape speed. But small primordial black holes could occur in clouds of gas and dust, from which stars formed. By the contraction of these gases, these black holes could become parts of some emerging stars from the beginning.
If such an inner black hole had the mass of a smaller planet, an inner accretion disk would form around it in the center of the star, and this accretion would generate a large amount of thermal energy. The radiant energy of such a star would no longer be powered only by nuclear fusion, but increasingly by the inner black hole as well. This process could be very long-term (~10⁶-10⁹years), with the black hole growing. In the late stages, this would lead to the cessation of fusion thermonuclear reactions in the core of the star and the expansion of the outer layers - establishing a star similar in appearance to a red giant, with a lower surface temperature. This star would then not perish in a supernova explosion, but by the continuous absorption - accretion - of all hydrogen and helium. A stellar-mass black hole would remain in its place. This hypothesis has not yet been confirmed...

Virtual black holes ?
As part of investigating the possibilities of the quantum theory of gravity, the virtual black hole hypothesis emerged, which exists temporarily due to quantum fluctuations in spacetime (quantum fluctuations in spacetime and spacetime foam are mentioned in §5.5 "Microphysics and cosmology. Inflation universe." and mainly in §B.4 "Quantum geometrodynamics") - they arise spontaneously and then disappear. Virtual black holes should have weights of the order of 10^-5 grams (Planck's mass) and would only exist for an extremely short time of the order of 10^-43seconds (Planck's time). Virtual black micro-holes have no astrophysical significance; if they existed, they could perhaps be important in quantum gravity and unitary field theory (§B6 "Unification of fundamental interactions. Supergravity. Superstrings."), or in elementary particle physics (§1.5 "Elementary particles and accelerators" in the book "Nuclear physics and physics of ionizing radiation") ..?..

What can be the maximum and minimum sizes of black holes ?
Black holes are very compact objects, so their spatial sizes (horizon diameters) are much smaller relative to their mass than other objects in the universe.
The largest black holes - gigantic "superholes" with masses of ~10⁶-10¹² M_¤ - are astronomically observed in the centers of large galaxies (the possibilities of their formation are discussed in more detail below "Mechanism of quasars and active galactic nuclei").
Black holes of intermediate masses ~10²-10⁴ M_¤ could form in regions with a tight cluster of more stars. They have not yet been observed, the competing mechanism of pair instability at the end of the evolution of heavy stars (Gravitace4-1.htm#ElektronPozitronNestabilita) may also apply here.
The minimum mass of a black hole formed by the gravitational collapse of a star, which is the only currently known formation mechanism, is around ~2.5-3 solar masses. ......
The very smallest black hole, according to the currently known laws of physics, could hypothetically have a Planck mass of about 0.02 milligrams. There is no known mechanism by which it could be created (quantum fluctuations of space-time are sometimes considered) and it would be immediately quantum vaporized by Hawking radiation - it would only be virtual.

Astrophysical behavior of black holes
We will now turn to the question of astrophysical behavior and the meaning of black holes, ie we will briefly analyze the processes of interaction of black holes with the environment in various situations that may occur according to astrophysical knowledge. The simplest effect of a black hole on the surroundings is the ordinary gravitational attraction between the black hole and the surrounding matter and bodies (stars). At distances substantially greater than 2M, the gravitational pull of a black hole is exactly the same as that of an ordinary star of the same mass. Thus, planet or another star may orbit a black hole along almost Kepler orbits - a black hole may be a component of a binary star or a multiple system. Stars "age" at different speeds (depending mainly on their mass), so in a binary system, one component may reach the black hole stage, while the other component may still be a normal star. At smaller distances from the black hole, relativistic effects are already evident: twisting of "perihelium" orbiting bodies, intense radiation of gravitational waves, possibility of absorbing bodies flying close enough around the black hole, gravitational lensing effect for light passing around the black hole, entrainment effects body by rotation of the black hole and the similarly.
What would happen if the Sun turned into a black hole?
Let's imagine in a fictitious thought experiment that our Sun would immediately turn into a black hole - peacefully, without an eruption of gases and radiation or a supernova explosion (according to the analysis in §4.2, we know that nothing like that is possible..!..). So that this black hole has the same mass (and possibly also the rotational moment of momentum) as the original Sun. What consequences would this have for our Earth and the planetary Solar System ?
-> First of all, Earth and the other planets would continue to orbit in exactly the same orbits as before. Gravitational attraction does not depend on the nature of matter-energy. which causes it. The orbit of the planets will not change until the mass of the central object, here the black hole, changes.
-> The sky would be as dark as the deepest night. Only distant stars would shine. We would not see the Moon or any planets because there would be no sunlight to reflect off them.
-> The surfaces of the planets and their atmospheres would cool down to a temperature of about 3 ºK in a short period of time, due to the absence of solar radiation (however, the deeper layers would retain accumulated heat for a long time and could be heated by tidal forces and the radioactivity of uranium, thorium, and potassium). Atmospheric gases (nitrogen and oxygen on Earth) would freeze and fall to the surface as "snow". On Earth all life would soon end... However, all this negative freezing changes for us would simply be due to the lack of solar radiation, but not due to the action of the black hole !
-> In the place where the Sun was, we would see nothing but an empty starry sky. The event horizon of a solar-mass black hole has a diameter of only about 3 kilometers, and gravitational-optical effects (analyzed in §4.3, passage "Gravitational lenses. Black hole optics") are limited to an area of about 4-6 km. They are too small in size to be seen at a given distance with the naked eye, or even with an ordinary astronomical telescope. However, precise astronomical measurements of the position of the stars would clearly register the effect of bending of the path of light by gravitational field of the central body - the black hole.
Limited "radius of action" of black holes
Black holes are locally very effective "vacuum cleaners" of matter from space - "bottomless abysses" from space. So we could expect a great destructive effect of black holes on the surrounding universe. However, this is not the case: black holes, due to their compactness, have a very small gravitational "radius of action" compared to cosmic scales - usually do not exceed the dimensions of the size of our solar system (§4.3, text around Fig.4.7). The black hole, as it moves through space, thus leaves behind only a very narrow trace "cleaned" of matter. If we compare it with the mentioned vacuum cleaner from everyday life, it would be an extremely powerful unit (vacuum pump) with a thin hose and a millimeter nozzle, which would perfectly vacuum the dust (and pull out even the carpet fabric), but only in this millimeter area...
But below we will see (in the section "Accretion disks, quasars, ..") that some specific phenomena in the accretion of matter into black holes can significantly prolong the astrophysical "radius of action" of black holes - but they are not gravitational action, but high-energy particles ejected from accretion disks at great distances into space.
The initially very small gravitational "radius of action" of black hole increases with time by two mechanisms :
- Growth in the size of the black hole (the horizon) as a result of accretion of matter.
- Emission of gravitational waves by each gravitationally coupled system at orbiting its parts around a common center of gravity. These gravitational waves carry away kinetic energy of the orbiting bodies, which are getting closer and closer until they finally merge.
Friction in the interstellar gas also contributes to this dissipative effect, by which part of the kinetic energy of the circulation is converted into heat, subsequently radiated out by electromagnetic waves, especially in the infrared range. On very long time scales (~10³⁵years), all galaxies will collapse into giant black holes. Only some stars that manage to gain more momentum will escape the galaxy and become lone "wandering stars". However, this process takes place on such large space-time scales that global cosmological metrics of space-time can be significantly applied here (some possibilities are discussed in §5.6 "The Future of the Universe. The Arrow of Time. Hidden Matter.").
Some potential risks from black holes are discussed in §4.9 "Complete gravitational collapse - the greatest catastrophe in nature", passage "Can a black hole engulf us and the whole universe?".

Emissions of gravitational waves in interactions with black holes
As described in §4.3 (passage "Emissions of gravitational waves when moving in a black hole field"), a body orbiting in a "stable" path around a black hole will lose energy by emitting gravitational waves, so it will (initially slowly) descend gradually in a spiral, until it reaches the innermost (lowest) stable orbit; then it is quickly absorbed by the black hole. The total amount of energy emitted by gravitational waves in such a process can be easily calculated if the mass of the trapped body m is much less than the mass M of the black hole. If such a body initially orbits in a distant orbit around a black hole, the amount of energy radiated by gravitational waves until the last stable orbit is reached will be given by the binding energy of this limit innermost stable orbit (we assume that all braking is caused by gravitational radiation): E₁^wave = m - E_ms, which for Schwarzschild the black hole is about 0.057 m (relation (4.21)) and for the extreme Kerr black hole it is about 0.423 m in the co-rotating circulation (§4.4, section "Particle motion in the field of a rotating black hole"). During the actual absorption of the body, a pulse of gravitational radiation with an energy of E₂^wave @ 0.01 m²/M is emitted (relation (4.22)). A body falling directly on a black hole emits in the form of gravitational waves the total energy of E^wave = E₂^wave, while a body descending gradually along a spiral radiates significantly more energy: E^wave ~ E₁^waves + E₂^wave. However, the most important gravitational-wave process is the emission of massive gravitational waves in close orbit in a binary system of black holes - it is discussed below in the passage "Binary systems of gravitationally coupled black holes. Collision and fusion of black holes .".
Destruction and absorption of bodies by black holes
The gravitational field in the vicinity of a black hole is strongly inhomogeneous, so that bodies moving near a black hole are subjected to large tidal forces, which can significantly affect the internal structure of these bodies. Stars flying around a black hole can be torn by tidal forces into parts, some of which are absorbed by a black hole, others can be ejected by reaction forces in stellar matter. If the black hole is rotating and this decay takes place in its ergosphere, the ejected part can also carry away part of the rotational energy of the black hole and gain considerable speed. The disruption of stars by tidal forces is even more effective in giant black holes, but it does not manifest itself externally, because it takes place already below the horizon (only there are sufficient tidal forces) - §4.2, section "External and internal view of gravitational collapse".

Accretion disks around black holes
The most important process of interaction of black holes with the environment *) is, however, accretion (lat. Accret = growth, enlargement, weight gain ), during which the black hole absorbs the surrounding material with its gravity and thereby increases own mass.
*) On the contrary, the least significant manifestation of black holes is probably quantum evaporation (discussed in detail in §4.7 "Quantum radiation and thermodynamics of black holes"), which is completely negligible in physically real situations (if we do not take into account primordial mini-holes, for which there is nothing does not indicate) and does not manifest itself - it is many times "overcharged" by the accretion of gases and radiation... Hypothetically, it can only manifest in the very distant future of the universe in the "heat death of the universe" scenario (§5.6 "The future of the universe. The arrow of time. Dark matter. Dark energy.").
Even a "lonely" black hole, located in the "vacuum" of interstellar or intergalactic space, absorbs cosmic radiation and slightly increases its mass. However, this unmeasurable phenomenon is not considered astrophysically relevant accretion. True accretion occurs when denser clouds of gas are found around the black hole. These can be clouds of gas after supernova explosions, large gas-dust regions in the center of galaxies (Fig.4.30), gas overflow from a star to a black hole in close binary systems (Fig.4.26).
Sufficiently dense surrounding matter, mainly gas, is drawn in by the powerful gravitational field and, during its fall onto the black hole, is heated to such a high temperature due to strong adiabatic compression and braking by viscous friction (this is accompanied by the formation of turbulence and shock waves), that there is a strong emission of not only infrared and visible light, but also X-rays from the inner part of the accretion disk. During accretion, an otherwise non-radiant black hole becomes a brightly shinning object ! More precisely, the glowing object is the absorbed gas in its vicinity.
The basic quantity describing the accretion is the accretion flux dM_A/dt, which is the amount (mass) of gas absorbed per unit time. However, the energy balance and intensity of radiation emitted during accretion also depends significantly on the mass and momentum of the black hole and the absorbed gas, as well as on the presence and intensity of the magnetic field (will be discussed below in the passages on thin and thick accretion disks).
The simplest type of accretion is spherical accretion, which occurs when the Schwarzschild black hole is surrounded by a non-rotating cloud of matter (gas). If the accretion flux dM_A/dt (which is the amount of gas absorbed per unit time) is sufficiently high, by adiabatic compression and viscous dissipation, the gas near the black hole will be heated to a high temperature and part of the energy will be radiated by electromagnetic waves. Gravitational radiation does not apply here, because there is no change in the quadrupole moment of mass distribution (which is, after all, zero in the considered spherical case) with time. In spherical accretion, the efficiency of converting the mass of the accreting gas to electromagnetic radiation is relatively low, so spherical accretion cannot be a sufficient source of quasar energy.
Spherical accretion is only the simplest idealized model, which is probably practically not realized. In fact, the particles of the accreting mass will always have a certain angular momentum with respect to the center of a black hole, so that the substance does not fall directly on it, but first orbits around it (if the particles of matter did not interact with each other, they would move in circular paths around the black hole). Especially in binaries systems (Fig.4.26) and galactic nuclei, the accreting gass will have a considerable specific angular momentum - significantly larger than it corresponds to circular orbits near the horizon. In this case, the absorbed gas around the black hole creates a rotating disc-like formation called an accretion disk - a cloud of gas that swirls and gradually sinks into a black hole. In this accretion disk, the gas revolves around a black hole, is braked by viscous friction (and magnetic braking, see below) and, after gradually decreasing circular - spiral - orbits, is directed towards the black hole. The radial rate of decrease of the gas particles is much lower than their rotational speed. In this way, a certain dynamic equilibrium is established in the accretion disk (unlike spherical accretion). The gradual fall of matter onto a compact object leads to the release of considerable gravitational energy, the emission of which also regulates the influx of new matter.

Fig.4.26. The formation of an accretion disk around a black hole, which is part of a tight "binary star". The equipotential surfaces that touch at the inner Lagrange point L form the critical Roche limit, which is the first common equipotential of a binary system (see §1.2, Fig.1.1d , passage "Binary system"). From a normal star, a gas stream can flow to a black hole through the Lagrange liberation point L, especially when the dimensions of the stars near the Roche limit. This gas enters almost circular orbits around the black hole, loses energy due to viscous friction and gradually descends to the black hole.
This image is a "top" view, in the direction of the axis of rotation of the accretion disk. The "side" view is in Fig.4.31.

If the black hole is rotating with a non-negligible angular momentum J, then due to the effect of entrainment of inertial systems (§4.4, section "Influence of black hole rotation. Ergosphere.") the accretion disk near the black hole will always be corotating and inclined into the equatorial plane of the black hole *); the circulating gas, even when coming from a direction different from the equatorial plane, is already pulled into the equatorial plane of the rotating black hole at a considerable distance by the effect of dragging of inertial systems.
*)The rotating space near the black hole entrains the inner parts of the accretion disk so that they are corotating and fixed in the equatorial plane, regardless of how they were oriented in the outer part of the disk. The configuration of the inner part of the accretion disk is independent of the dynamics of the gas trapped in the outer parts of the disk.
However, the outer areas of the accretion disk, further away from the black hole, may orbit at other angles, outside the equatorial plane, or the rotation of the gases may temporarily occur in the opposite direction - compare with the particle trajectory in Fig.4.15c in §4.4, section "Influence of black hole rotation". These circumstances depend on the direction from which the gas is coming, its momentum and the impact parameter.
By the way, the gas absorbed from the circulating accretion disk (which always has a non-zero angular momentum) introduces a certain additional rotational momentum into the black hole. Even if the black hole hole was originally non-rotating (static Schwarzschild), the accretion would gradually make it a rotating Kerr black hole ...
Non-accretion dark matter disks around black holes ?
The massive gravitational field of black holes affects not only ordinary matter, but also the ubiquitous hidden-dark matter (§5.6, section "Future development of the universe. Hidden-dark matter."). Therefore, a gravitationally bound disk of rotating dark matter can form around massive compact objects such as black holes, but with practically no accretion. Due to the absence of friction, the orbiting dark matter cannot get rid of excess angular momentum in any way and therefore cannot descend to progressively lower orbits to finally be absorbed by a black hole (cf. "Accretion discs around black holes" above); will continuously orbit around. This phenomenon can be expected especially for supermassive black holes in the center of galaxies, where a greater concentration of dark matter is assumed and the dark-matter rotating disk can be very massive. Even if it does not directly contribute to accretion, its gravity can greatly influence the structure and dynamics of an accretion disk made of ordinary matter.

Thin accretion disk
If the total weight of the disk is much less than the weight of the black hole (ie the own gravity of the mass of the disk can be neglected) and the accretion flux is not too high, it will be a thin accretion disk [193], [227] whose thickness is less smaller than its diameter - Fig.4.27 :

Fig.4.27. When accreting a gas with a specific angular momentum substantially greater than that of circular orbits near the innermost (lowest) stable circular orbit, the absorbed gas forms an accretion disk around the black hole, which is thin at low accretion fluxes. The gas particles move approximately in circular geodesics, being inhibited by viscous friction and gradually decreasing in a spiral up to the limit innermost of stable circular orbit r = r_ms, from where they are absorbed.

Braking and transfer of angular momentum in an accretion disk
The gas particles in the accretion disk move approximately in circular geodetic orbits. If they moved freely without interactions (collisions) with surrounding gas particles, they would orbit like this "forever", no accretion could occur. However, gas particles move faster on the inner orbits than on the outer orbits (as follows from the classical Kepler's laws; there will be even greater velocity gradients in the relativistic case). During particle collisions on "adjacent" orbits, the inner particles are braked and the outer ones are accelerated - the angular momentum is transferred from the inner part to the outer part of the disk. The inner particles thus descend into an orbit closer to the center, the outer ones rise to a more distant orbit. The kinetic energy that the particles gain from these collisions heats the gas, which then emits radiation (discussed below).
Thus, due to the viscous friction *) between the outer layers, the gas particles in the inner layers are thus braked, the radius of their orbits slowly decreases and the mass thus gradually decreases towards the black hole. After reaching the limit of innermost stable orbit r = r_ms, which is the inner edge of the thin accretion disk, then the gas falls rapidly into the black hole. If there are no major inhomogeneities in the accretion disk, the emission of gravitational waves does not occur, because (similarly to spherical accretion) the quadrupole moment does not change with time. In this process, there is a current of angular momentum from the inner layers of the disk to the outer layers (rotation of the outer layers is accelerated by friction), where part of the mass is released and carries away the excess angular momentum. Viscous friction heats the disk (especially in the inner parts) to a high temperature and this energy is radiated out by electromagnetic waves.
*) The difference between the velocities during circulation on the higher and lower orbits leads to a certain "velocity shear", which according to the laws of hydrodynamics causes turbulence in the circulating gas flow. These turbulences lead to even sharper collisions of larger volumes of gas, more efficient energy dissipation and higher accretionary flux. Astronomically observed brightness fluctuations of the respective objects suggest that turbulence in the accretion disks is indeed taking place.
Magnetic transfer of angular momentum
The shear friction in the thin gas is relatively weak and may not be sufficient for the necessary mechanical transfer of the orbital angular momentum from the interior of the accretion disk towards the peripheral parts (however, this friction is probably sufficient to heat the inner dense and fast regions of the accretion disk to high temperatures, as discussed below). However, if the accreting gas is partially ionized (which is generally expected), there may be a strong magnetic field. The inner, rapidly rotating parts of the accretion disk act as an "engine" generating a rotary magnetic field, which then electromagnetically spin up the outer parts of the accretion disk *). And the rotation of the internal parts of the disc are adequately braked by this. The transfer of angular momentum from the inner part to the outer part of the accretion disk can thus take place effectively even without direct mechanical contact between these areas.
*)It is somewhat similar to an external coil powered by an alternating current, creating a rotating magnetic field that electromagnetically spins the anode of the X-ray tube through the vacuum, without mechanical contact with it (passage "X-ray tubes" Fig. 3.2.3 in §3.2 in the monograph "Nuclear Physics and Physics of Ionizing radiation").
Energy release in the accretion disk
Under the circumstances common in our terrestrial conditions, friction is not a very powerful source of heat (let's try, for example, to start a fire by rubbing wood...). In the accretion disk, however, there is an effective high-speed "friction" (precipitation) of gas particles accelerated by a enormous gravitational energy, substantially greater than nuclear energy. Therefore, friction effectively heats the disk so much, that it can glow more than stars (even the entire galaxy, as will be shown below in the section on quasars).
Note: Accretion disks can also form around neutron stars or white dwarfs, but their energy efficiency is significantly lower than that of black holes (the specific binding energy of particle orbits at the surface of such stars is relatively small).
At equilibrium, the total radiated power is equal to the amount of energy that all particles in the disk generate per unit time by internal friction. Each gas particle of mass dM as it passes through the whole disk from its originally large distance (in which we can neglect the gravitational binding energy) along the spiral path to the boundary - last - stable orbit r = r_ms (Fig.4.27) gives the disk viscous friction energy equal to its binding energy at the limit innermost stable orbit. The total power emitted by the disk (luminosity) is therefore equal to

where dM_A/dt is the total accretion flux and` E _ms is the specific energy in orbit along the innermost (lowest) stable circular path. The "efficiency" of the conversion of the rest mass of the accreting substance into the radiated energy is thus given by the specific binding energy 1-` E_msof the innermost stable orbit. For the non-rotating Schwarzschild black hole, this efficiency is approximately 5.7%, but for the extremely rotating Kerr black hole it is about 42.3% (see §4.4)!
Therefore, if the black hole initially has a slow rotation and the energy efficiency of the accretion disk is around 5.7%, this efficiency will slowly increase over time as the black hole is gradually "more-rotated" by the transmitted angular momentum of the absorbed mass *). Change of mass and angular momentum black hole into which the material falls from the innermost stable orbits specific energy` E_ms and specific angular momentum` L_m given by expression (4.39) with r = r_ms leads to the fact, that a black hole can be spin-up by the theoretically up to the extreme state J = M² (limit given by the 3rd law of Black Hole Mechanics, derived in §4.6 "Laws of Black Hole Dynamics"). In reality, however, part of the radiation from the accretion disk is absorbed by the black hole, and this absorbed radiation will somewhat inhibit the rotation of the black hole, because the effective cross section of capturing photon moving against the direction of rotation of the black hole is larger than for photons corotating. As a result, the limit rotation will be slightly slower, about J @ 0.918 M² [215], and the conversion efficiency accreting material on the radiation disc will reach a limit around 30%; such a black hole with the maximum achievable speed of rotation, driven by transmitted angular momentum of the accretion disk, is sometimes called canonical.
*) The gas falling in a spiral into a black hole brings angular momentum and spins it at ever-increasing speeds. When the black hole about twice doubles its weight by this absorption, it reaches almost critical "extreme" rotational speed; then the already centrifugal forces prevent further acceleration of the rotation (§4.4, section "Movement of particles in the field of a rotating black hole"). Large black holes that have grown due to accretion should have almost maximum rotation speed (extreme, more precisely "canonical").
At large accretion fluxes and thus large radiative powers - especially when the radiated power is close to the limit Eddington luminosity W_Ed = 4p G.M.c/O (» 1,3.10³¹M/M_¤ [J.s^-1] (if the opacity O is caused by classical Thomson scattering in ionized gas; was derived in §4.1) - in the inner region of the disc the radiation pressure becomes dominant over the gas pressure. To meet the condition of mechanical equilibrium, the flux of radiated energy at each location must be less than the corresponding "critical" flux (at which the radiation pressure would equal the resultant of gravitational and centrifugal forces); this critical radiation flux is directly proportional to the total gravitational acceleration at a given location and indirectly proportional to the opacity of the accreting mass. For high accretion fluxes, the thin accretion disk model is no longer adequate, the disk with increasing accretion flux begins to "get fat". Pressure gradients are significant manifested here, the movement of gas particles no longer takes place along almost Kepler orbits; it will be a thick accretion disk [145], [1], [227], [37] :

Thick accretion disks. Quasars.
The shape of the accretion disk in this situation is schematically shown in Fig.4.28. The disk remains thin at great distances and also at the inner edge, from where the mass overflows into a black hole. The inner edge of the disk no longer lies in the limit innermost stable orbit, but is shifted somewhat deeper; the radius of the inner edge of the disk lies between the innermost stable circular orbit r = r_ms and the limit circular orbit r = r_f, where it is pushed by the pressure gradient. The total radiated power is again given by (4.66), where instead of` E_ms a specific energy corresponding to the orbit of the radius of the inner edge of the disk emerges. The higher the accretion flux dM_A/dt, the "thicker" the accretion disk, the steeper its inner walls and the more the inner edge of the disk shifts toward to the boundary (photon) circular orbit r = r_f. With increasing accretion flux, the total radiant luminosity of disk increases, although the conversion efficiency of conversion of absorbed material to radiant energy decreases somewhat, because the absorption of of matter by a black hole occur from orbits lower than the innermost stable circular orbit (which has the greatest binding energy, see §4.4) and binding energy is lower here.

Fig.4.28. At high accretion fluxes, the accretion disk around the black hole becomes thick and its inner edge lies below the marginal innermost stable circular orbit. Most of the dissipation energy is radiated by the inner walls of the disk, which at considerable thicknesses are quite steep and form a "funnel" around the black hole. At the bottom right is a directional radiation pattern of a thick accretion disk. The vast majority of radiation is collimated in the direction of the axis of rotation (coming from the "funnel" of the accretion disk).

For very large accretion flows, considerably thick accretion disks with high and steep inner walls are formed; these steep walls of the accretion disk form a kind of double "funnel" around the axis of rotation, in the center of which lies a black hole (Fig.4.28). Because most of the energy generated by the disk is radiated by these inner walls (multiple absorptions, scattering and re-emission of radiation also occur on the inner walls), the resulting disk radiation will be strongly non-isotropic: most radiation will be emitted by a "funnel" in narrow cones along the axis of rotation. If such an accretion disk is observed from a direction only slightly different from the direction of the axis of rotation, its apparent luminosity may exceed the Eddington limit many times over (super- Eddington luminosity). In addition, the strong flux of radiation in the "funnels", by its pressure, can accelerate on the relativistic velocity the gas particles, that got out of the disc walls ("jet effect"). This creates mighty cosmic jets - collimated streams of ionized gas and high-energy particles, flying in both opposite directions along the axis of rotation of the accretion disk. Furthermore, the interaction of high-energy particles can produce gamma radiation, also emitted in a narrow cone along the axis of rotation. The direction of gas and radiation streams is thus firmly and long-term tied to the axis of rotation of the black hole. Cosmic ray acceleration mechanisms could work in black hole jets. Turbulence in the accretion disk can lead to shock waves, in which conditions are created for the acceleration of particles even to the highest energies. Jets from the interior of rotating accretion disks of black holes could thus be (in addition to supernovae) a significant source of cosmic radiation - high-energy charged particles, especially protons, spreading over long distances in space.
For the properties of cosmic radiation, mechanisms of origin, its propagation, possibilities of detection and influence on life, see §1.6 "Ionizing radiation", part "Cosmic radiation" of the book "Nuclear physics and physics of ionizing radiation".
Furthermore, jets from accretion disks of giant black holes of active nuclei of galaxies interact with intergalactic matter, containing atoms of hydrogen, helium, carbon, oxygen, etc. The kinetic energy of jet particles heats the gas of intergalactic matter and supplies activation energy for many chemical reactions water, carbon dioxide, hydrocarbons, etc. It thus cooperates (together with gas emissions from stars, supernova explosions, with cosmic radiation) in the chemical evolution of the universe.
The speed of rotation of the accretion disk and the intensity of mass jets
The intensity of the jets significantly depends on the speed of rotation (angular momentum) of the black hole. With slow rotation, only faint jets are produced, most of the gas from the accretion disk quickly proceeds to the black hole, where it disappears forever. However, rapidly rotating black holes eject up to 25% of the gas that enters the accretion disk.

Radiation spectrum from accretion disks
It was discussed above how in the accretion disk the gas is drawn in by a massive gravitational field and as it descends to the black hole it heats up to such a high temperature due to strong adiabatic compression and braking by viscous friction that not only infrared and visible light is emitted, but from internal parts of the accretion disk even X-rays. Also, the chaotic turbulence of the plasma, with the participation of magnetic fields, strongly locally heats the plasma in the accretion disk, which leads to the emergence of X-radiation.Above all, intense radiation in the form of collimated jets is emitted from inside the narrow funnels along the axis of rotation. UV funnel and high-energy electrons are also generated in the funnels inside the accretion disk. During the interactions of photons with electrons, multiple Compton scattering of photons on fast electrons *) can occur, during which the energy of UV photons can increase up to the level of X-rays, the intensity of which is stronger the stronger the radiation from the accretion disk. Thus, heavier accretion disks should emit a higher proportion of harder photon radiation.
*) The standard Compton scattering of photon radiation (gamma or X) in substances takes place on electrons that are essentially at rest, while the energy of scattered photons decreases (see §1.6, passage "Interaction of gamma and X radiation", paragraph "Compton scattering" in book "Nuclear Physics and Ionizing Radiation Physics"). However, during scattering on fast electrons, the energy of some photons may increase, if the scattering occurs approximately in the direction of electron motion (referred to as the inverse Compton effect).
The electromagnetic radiation emitted by the accretion disk has a basically continuous spectrum from radio waves, through infrared, visible and UV radiation, to X-rays. The different parts of the disc have very different temperatures. In the innermost parts, where the temperature reaches up to 10⁶-10⁸°C, there can be no atoms exists and the rapidly moving electrons in the fully ionized plasma generate braking X-rays with energies of unit up to tens of keV. In slightly higher layers, where the temperature is lower than about 3000 °C, atomic nuclei can already keep electrons in the shell. These electrons are then excited by the primary X-rays from the inner region of the disk and, upon deexcitation, emit secondary characteristic X-rays with a line spectrum (lines K_a,b). However, due to the gravitational and Doppler frequency redshifts, this line will be greatly widened, especially to areas with lower frequencies. Indeed, such an extended spectral line X of the K_a-Fe of the iron atom was observed in the radiation spectrum of the galaxy MGC-6-30-15.
Radiation from the inner part of the accretion disk occurs mainly in the X-ray spectral region. Thus, X-ray spectrometry may be one of the ways to determine the rotational speed and other parameters of the accretion disk. For this analysis, the characteristic X-radiation of the gas atoms in the accretion disk can be particularly useful. The spectral lines of the characteristic X-rays of gas atoms from the inner part of the rotating accretion disk are significantly wided by Doppler effect by fast orbital motion (thermal spread of spectral lines caused by chaotic motion of individual gas particles is much smaller in this case than Doppler schift by fast motion in accretion disk). In addition, the fundamental natural frequency (energy) of the photons w_o when reduced from a great distance (A) is reduced by the gravitational redshift relative to the known laboratory energy. The remote observer measures the reduced value of the frequency w_A. The effect of the gravitational frequency shift from the general point of view of GTR is briefly outlined in §2.4, passage "Gravitational spectral shift". Here, it depends on the angle at which the accretion disk is oriented relative to the distant observer :
A remarkable special arrangement is the "frontal" orientation of the accretion disk, with the axis oriented to the observer. In this case, the gravitational redshift from a point at a distance r in the accretion disk is w_o/w_A = 1/Ö(1-3M/r). In the inner part of the disc, at the lowest stable circular orbit r = r_ms~ 6M, the gravitational frequency shift is w_A = w_o/Ö2 = 0,7.w_o. Doppler frequency shift is not applied here.
A slightly more complex situation can be expected for accretion disks tilted towards the observer "from the side" (with their "edge"). In addition to the gravitational spectral shift, the Doppler frequency shift will also be significantly applied here - by a factor of [1 ± 1/Ö(r/M - 2)], where the "+" sign applies to the emitting atom moving in the accretion disk away from the observer and the " - "corresponds to the emitting atom moving in the opposite part of the accretion disk towards the observer. In the inner part of the accretion disk with r = r_ms ~ 6M this corresponds to the range w_A» (0,93¸0,47).w_o. Due to the high rotational speeds, the observed spectral lines should therefore have a split shape with two peaks and a drop in the middle. One of the peaks occurs in the part of the disk where the gas moves towards the observer, while the other peak comes from the area where the gas moves away from the observer. The representation and energy spacing of these split peaks would depend on the inclination of the rotational plane of the disk with respect to the direction of the observer.
A certain observed spectral line of characteristic X-rays is composed of photons coming from different regions of the accretion disk with different radii r. Since the value of the gravitational redshift depends on the distance r of the emitting atom from the center of the disk and is different for different geometric orientations of the accretion disk with respect to the observer, by analysis the energies and shape of the measured spectral lines of the characteristic X-radiation we can approximately determine the size of the accretion disk and its orientation with respect to the observer.
Astronomical X-ray spectrometry is still in the beginning. However, future sensitive spectrometers located on space probes will certainly be able to measure fine details in the radiation spectra of accretion disks around black holes (or neutron stars) and thus determine the rotational parameters of accretion disks and thus the black holes themselves.

Electromagnetic extraction of black hole rotational energy
A black hole as such does not have its own magnetic field (see §4.5 "A black hole has no hair"). However, the charged particles swirling in the plasma of the accretion disk around the black hole represent an effective electric current generating a magnetic field. The strong magnetic field created in this way probably plays an important role in the formation of jets from the accretion disk of a rotating black hole.
Its lines of force are entrained by the rotation of the black hole and lead to the induction of intense electric forces acting on charged plasma particles in the direction along the rotational axis of the black hole. It accelerates these particles at the relativistic speeds. The tightly coiled magnetic field that wraps the jet keeps it in the shape of a narrow beam with little divergence. In this way, the jet continues by inertia to distances of hundreds and thousands of light years - it rushes through the interstellar space of the parent galaxy, leaves it and penetrates into intergalactic space. Only at very great distances does the jet slow down, expand, swell and form large glowing clouds high-energy particles (Fig.4.29) interacting with the surrounding gas. Electrons with a velocity close to the speed of light in an ionized gas orbit in spirals around magnetic field lines and emit electromagnetic waves - synchrotron radiation (the mechanism of synchrotron radiation is outlined in §1.6, passage "Cyclotron and synchrotron radiation" of the book "Nuclear Physics and Ionizing Radiation Physics", see also Fig.4.3 in §4.2, part "Pulsars - fast rotating neutron stars").
The mechanism of a gigantic "MASER" - stimulated emission of radiation in more distant atoms under the influence of harder radiation from the central parts of the disk - could also contribute to the observed massive radio radiation.
In addition, a very strong magnetic field in the central part of the accretion disk (which could reach up to 10¹⁰T) can cause fast charged particles, especially electrons and positrons, point in to negative energy orbits in the ergosphere of a rotating Kerr black hole, which could lead to the extraction of the rotational energy of a black hole by the Penrose process - the so-called Blandford-Znajek mechanism [20], see §4.4, part "Penrose process", passage "Electromagnetic extraction of rotational energy - Blandford-Znajek mechanism".
When a plasma of charged particles orbits a rotating black hole - the accretion disc, it creates a strong poloidal magnetic field by rotating toroidal currents flowing in the equatorial plane. The entrainment of space, and thus of the magnetic field lines by the rotation of a black hole, then induces an intense electric field - a powerful electric generator is created in the form of a stream of charged particles. Some of them enter orbits with negative energy in the ergosphere and fall into a black hole, while the extracted energy strengthens the electromagnetic field. Other charged particles are then electromagnetically accelerated by the extracted rotational energy and transfer this energy to the plasma in the jets by magnetohydrodynamic effects. Such a "gravito-magnetic dynamo", driven by the rotation of a black hole, could supply a considerable amount of energy to the jet from the accretion disk, contributing to the relativistic jets from inside the accretion disk.
The rotating accretion disk around the black hole thus acts as a kind of rotating-linear "jet engine", converting part of the mass falling into the black hole into high-energy quantum and particles, radiated linearly along both axes of the black hole. The efficiency of this engine can reach up to 30% (from mc²) *) for fast-rotating black holes; existing jet or rocket engines can only envy this efficiency! "Mega-jets" from giant black holes in the center of galaxies, surrounded by massive accretion disks, are the most energetic processes we observe in the universe!
*) The energy of the jets is partly drawn from the rotational energy of the black hole (§4.4, part "Penrose process"). However, the rotational energy of a black hole is continuously supplemented by the accretion of the co-rotating gas, which brings the angular momentum. The accreting mass can store almost 30% of its rest energy in the rotating gravitational field around the black hole. And this huge energy can then be pumped from there via the accretion disk to the kinetic energy of the high-energy particles in the jets. This is the essence of the "black hole engine" that supplies quasars and massive gas currents in the lobes of radiation-active galaxies :

The mechanism of quasars and active galactic nuclei
The idea of a thick accretion disk around a large black hole (Fig.4.28) so quite naturally explains the most important peculiarities observed in quasars and radiation active galactic nuclei, ie. their extreme luminosity (highly super-eddington) and ejected clouds of relativistic particles in the form of massive jets - Fig.4.29 :

	In the 3C449 radio source, jets are about 200,000 light-years long from the core of an elliptical galaxy. The galaxy is about 150 million worlds away from Earth. flight.
	In a 3C348 radio source, about 1.5 billion away from the light-years, the jets form a structure as long as 1.5 million light-years!
Fig.4.29. Examples of radio astronomically observed jets from active galaxy nuclei.

In quasars, the central black hole in the galaxy is intensively "fed" by the surrounding absorbed gas, and there is great friction in the gas in the massive accretion disk. The large amount of heat heats the disk so much, that with its brightness of 100-x and 1000-x it overcomes all other stars in the galaxy. The innermost part of the disk is so hot that it emits mostly X-rays, further from the center the disk is colder and emits UV radiation, then visible light. In the outer parts, the disk is already relatively cold and emits infrared radiation. Massive streams of gas, heading from the accretion disk to the intergalactic environment, radiate energy in the area of radio waves.
A more detailed explanation of the astrophysics of accretion disks goes beyond the scope of this book focused on relativity, gravity and spacetime (we can refer, for example, to the recently published review work [37] and the literature mentioned there). Significantly complicated models of accretion disks are constantly evolving in an effort to move from phenomenological character to the application of laws of microphysics leading to finding the equation of state, viscosity mechanisms, turbulence, magnetic effects, opacity and other processes of dissipation and energy transfer, co-determining disk shape and dynamics, flow distribution radiation and its spectra from the surface and from inside the "funnel" of the accretion disk.
To summarize, currently the most realistic model of a quasar is the following notion (Fig.4.30): A quasar is an extremely active nucleus of a galaxy that is collapsed into giant black holes weighing ~10⁶-10⁹M_¤. Around this black hole, a thick accretion disk is formed from the surrounding matter (interstellar matter and disturbed stars), in which the gravitational binding energy of the absorbed matter is converted into radiant energy. These radiation active galactic nucleus may radiate more intensely than the entire galaxy, wherein the radiation is strongly anisotropic - directed along the rotation axis of the disc - and a time variable (due to inhomogeneity and turbulence in the accretion disk). Thanks to the sharp anisotropy of radiation from the thick accretion disk, a selective effect is manifested: we see mainly those quasars that are to us inverted by its axis of rotation (observer "A" in Fig.4.30) :

Fig.4.30. Intense jets of relativistic particles and radiation gush from a massive accretion disk around a rotating massive black hole in the center of a young galaxy along the axis of rotation. The distant observer "A", to which the system is inclined by the axis of rotation, observes a clear point source - the quasar. The lateral observer "B" then sees the radiation - active nucleus of the galaxy with jets of ionized gas.
Note: In the illustrative drawing, the dimensions of the black hole and the accretion disk are greatly enlarged relative to the size of the galaxy (the black hole and the accretion disk are many billions of times smaller than the galaxy...).

Their luminosity then appears to us many times greater than would correspond to isotropic radiation. In addition, in the case of plasma clouds ejected from the "funnel" of the accretion disk, a special relativistic selection effect is also taken in that the radiation of the fast-flying source appears to the observer in a cone in the direction of movement; the rapid movement towards the observer is also related to the seemingly superluminal velocities observed in the ejected clouds from inside the quasars. The intense flux of radiation completely overexposes the rest of the galaxy, which is usually not visible at all, we see only a point object (observer "A").
If the accretion disk around the giant black hole is not to us inverted by its axis of rotation, we do not see closely collimated intense radiation from inside the accretion disk. In this case, we do not observe a quasar, but a distant galaxy with a radiation - active nucleus (such as Seyfert's or radio galaxies), from which massive streams of ionized gas gush to opposite sides (observer "B" in Fig.4.30).
Quasars (+ blazars) and active nuclei of galaxies probably represent the same phenomenon in outer space - radiation from rotating accretion disks around giant black holes in the center of galaxies, which is only observed from a different angle *), depending on the inclination of the plane of the accretion disk relative to the line of sight.
*) Different angles of view: The difference between the observational perception of the accretion disk around a massive black hole in the core of a distant galaxy, when viewed in the direction of the axis of rotation and in a different direction, can be roughly compared to the night observation of a car. When the car is driving in the distance against us, we only see bright spotlights, which overexpose the faint image of the car. However, if we observe a glowing car from the side (it goes along a side road, for example), we see traces of light cones in the air and the surrounding terrain, sometimes partly the outlines of the car itself.
Similarly, if we observe a galaxy with an active central black hole "from the side", at an angle to the axis of rotation close to 90°, it appears as a radiogalaxy with jets, at angles around 60° as a Seyfert galaxy. At angles less than 30°, intense radiation from the jet overexposes the image of a distant galaxy, and the object appears as a bright glowing point similar to a star - a quasar. When viewed at a very small angle almost in the direction of the axis of rotation, we see the clearest effect, referred to as the blazar (mentioned above in the passage "Quasars and active nuclei of galaxies"); the variability of radiation intensity is also best seen here.

Superluminal velocities of jets from quasars ?
If there is any astronomically observable distinct structure in the jet, we can determine the speed of movement of this structure in the sky by precisely observing its position A, B at two times t₁, t₂ (a few months apart) - in principle, thus we measure the speed of the gas in the jet. Detailed measurements of the light (and electromagnetic radiation in general) of jets from quasars and active galactic nuclei have shown that in many cases the movement of the glowing gas structures in the jets appears to be faster than light. This deceptive effect occurs when the velocity of the jet is close to the speed of light (>0.9c) and there is a high component of the velocity towards the Earth (small jet angle q approx. 10°-40°). In such a case, as the observed structure in the jet moves towards the Earth, the distance d₂ is shortened compared to d₁ and thus the time delay of detection in both positions A, B by the value (v/c).cosq. As if the observed structure had managed to overcome the distance between the two places A-->B earlier. This means that the apparent observed velocity v´ appears larger than the actual velocity v, by the ratio 1/[1-(v/c).cosq].
Apparently superluminal velocities in the inner parts of jets have been observed, for example, in quasars 3C 273, 3C 279, M87, ....
The issue of astronomically observed apparently superluminal velocities is discussed in general in §1.6, the passage "Apparently superluminal speeds of motion?", from which we reproduce the image here for clarity :

Active and "starved" quasars
It is likely that very massive black holes "reside" in the center of most galaxies. However, not every such black hole is reflected by the massive radiation of the surrounding gas, such as a quasar or an active galactic nucleus. This requires a sufficient supply of material to the accretion disk. In many cases, the "feed supply" is probably insufficient and the black hole is "calm", inactive. From this point of view, it is characteristic that we observe most quasars in the distant universe, which also corresponds to the distant past when the universe was only about 2-4 billion years old. In the distant past, young galaxies contained far more gas and dust than they do today, so the central black hole had a much greater supply of material for the massive accretion disk in the long run. After depletion of this supply of gas and dust in the central part of the galaxy, the accretion gradually ceased, the massive quasar "starved" and faded; now the surrounding galaxies, including ours, are relatively peaceful.
However, such an inactive black hole, or "starved quasar", may again "wake up" for a while if a star or a large gas-dust cloud wanders near it, from which the black hole "sucks" a new supply of material by gravity. If a normal star (solar type) gets close to a black hole (mass ~10^6-9M_¤), will be torn and destroyed by massive gravitational tidal forces *). As it approaches, the tidal forces will initially stretch it in the direction of orbit. Upon further approach, the tidal forces overcome the star's own gravity and tear it into thin arcuate gas streams. This gas enters an ever-lower orbit and, before being absorbed, forms a hot accretion disk from which intense radiation and energetic particles are emitted along the axis of rotation - for a "shorter time" a quasar or an active galactic nucleus is formed again. Something similar may have happened to our Milky Way galaxy. The observed giant clouds of gas (so-called Fermi bubbles) extending to both sides from the center of the galaxy could have arisen in such a way, that a few million years ago the intensity of accretion to the central black hole suddenly increased and the resulting energetic polar jets interated with the surrounding thin gas and created these bubbles.
*) However, small and dense compact objects - white dwarfs and neutron stars, or smaller black holes - are much more resistant to tidal forces than solar-type gaseous stars, so they can be absorbed by the black hole "as a whole". A weaker accretion disk could only arise here from gases or planets that orbited them.
The most gigantic black holes of mass > ~10¹¹M_¤ have gravitational gradients (tidal forces) at their horizon too weak to rupture incoming stars and form an accretion disk that would be a source of radiant energy and quasar jets. Such a gigantic black hole "swallows the stars as a whole", without the formation of a more massive accretion disk and thus without quasar effects (after depletion of the initial gas supply from its surroundings). The largest black holes are probably not quasars ..?.

The spectrum of quasar radiation
In the section on thick accretion disks ("Thick Accretion Disks. Quasars."), it was discussed how intense radiation is emitted inside narrow funnels along the axis of rotation in the form of narrow jets. In the funnel inside thick accretion disk arises also UV radiation and high-energy electrons. When the interactions of photons with electrons may occur for multiple Compton scattering of photons at fast electrons *) in which can increase energy UV photons to the level of X-radiation whose intensity is higher, the emission from the accretion disk larger. Thus, brighter quasars should emit a higher proportion of harder photon radiation.
*) The standard Compton scattering of photon radiation (gamma or X) in substances takes place on electrons that are essentially at rest, while the energy of scattered photons decreases (see §1.6, passage "Interaction of gamma and X radiation", passage "Compton scattering" in book "Nuclear Physics and Physics of Ionizing Radiation"). However, during scattering on fast electrons, the energy of some photons may increase if the scattering occurs approximately in the direction of electron motion (referred to as the inverse Compton effect).
Quasars as "standard candles" in the farthest universe ..?..
Quasars are the only observable objects in the outermost universe. The absolute magnitude (actual radiant power) of quasars is different, it depends on the mass and rotational angular momentum of the black hole and especially on the amount of absorbed gas - accretion flow. However, as shown above, this absolute magnitude is related to the emission spectrum of the quasar, especially to the ratio of radiation in the ultraviolet and X-ray fields. At present, these spectrometric measurements are performed on a number of quasars of different distances, which will make it possible to determine the calibration dependence between the spectrum and the absolute magnitude of the quasar. Once the true luminosity is known, the distance of the quasars can be determined from the observed radiation intensity. The quasars can then be used as "standard candles" for measuring the greatest cosmological distances (where it can supplement and replace type Ia supernovae, see §41.1, passage "Determining the distance of space objects") .
How did central supermassive black holes form ?
The question remains, by what mechanism and at what stage of evolution galaxy, these central supermassive black holes formed? What came first - galaxies, or their central black holes? There are basically three standard hypothetical options; a fourth possibility is the inclusion of hypothetical dark matter :
1.In the dense gas in the center of early (proto)galaxies originated many massive stars *), which quickly exhausted its nuclear fuel and collapsed (over supernova explosion ) into black holes weighing tens to hundreds of M_¤ - a kind of "seed black hole", which have become "germs" for the formation of supermassive black holes. These medium-sized black holes then absorbed the surrounding gas (and possibly the stars) and in a dense environment their orbital motion was effectively braked. Therefore, they merging to each other relatively quickly, creating seed black holes weighing about 10 000 - 100 000 M_¤. For several hundred million years, they could grow into giant masses, which were further increased by accretion. However, with this scenario of the gradual merger of many small black holes of stellar masses, the observed supermassive black holes at the center of galaxies could take many billions of years to form.
*) At that time there was only hydrogen and helium in the universe, the stars of the first generation had zero metallicity and could have formed with masses of tens or many hundreds of M_¤.
2.A very large clouds of dense gas (and dark matter..?..) in the center of the emerging galaxies could collapse directly into a large black holes, without the need for star formation and evolution - without collapse into black holes of stellar masses. Especially during the collisions of massive streams of cold gas, large-scale condensations could form, which could collapse into very massive black holes. These "gembrinal" black holes could have masses of many tens of thousands to several million M_¤ and could be surrounded by a larger number of 1st generation stars - the star clusters. The collisions and mergers of a larger number of these seed black holes could have produced supermassive black holes in a cosmologically relatively short time (several hundred million years). And in addition, there is a possible scenario that the gradual fusion of the surrounding star clusters could also have created the galaxies themselves with a gigantic black hole in their center..?..
3.In a hypothetical scenario, there may first have been large primordial black holes (as mentioned above in the passage “Primordial black holes?"), around which the first galaxies formed, within which they then increased with accretion and formed supermassive central black holes..?.. There is no astronomical evidence for this hypothetical scenario.
Many observed quasars are very old, probably formed about 200 million years after the beginning of the universe. With the help of commonly observed matter, we cannot yet convincingly explain how such gigantic black holes could have formed so soon after the beginning of the era of substance..?..
4.But it is likely that in the gravitational collapse of large gas-dust clouds and possibly merging of the resulting seed black holes was hidden-dark matter significantly involved (its existence and properties are discussed in §5.6, section "Future evolution of the universe. Hidden-dark matter."), whose attractive gravitational effects prevailed over the repulsive pressure forces in vast contracting gas clouds..?.. At the time of the formation of the first galaxies and stars, about 200 million years after the creation of the universe, the primordial dense clouds of hydrogen and helium could contain a significant percentage of dark matter. Dark matter, due to the absence of pressure, could gravitationally clump together earlier than the atomic-baryonic matter of hydrogen and helium gases. And it was only against the background of these dark matter densities, invisible to us, that the observed large-scale structures in the universe condensed..?..
It is discussed that, with the participation of dark matter, the first emerging stars of the 1st generation could hypothetically reach large masses of up to millions of M_¤. After their early collapse, they could also be the seeds for the formation of supermassive black holes..?..
Observation of some very distant and therefore early galaxies, formed about 500 million years after the big bang (or even earlier), shows that the mass of their black holes is comparable to the total mass of their stars. It indicates that at least some giant black holes were created by scenario No. 2 (or 4) - the direct collapse of massive clouds of gas. And these galaxies then grew around these central black holes.
Discussion on the topic "Which came first: galaxies or giant black holes at their center?" is also outlined in §5.4, section "Formation of the large-scale structure of the universe", passage "Structure and evolution of galaxies".
The occurrence of large black holes and their role for galaxies
Two questions are sometimes debated :
1. "Does every galaxy have a supermassive black hole at its center ?"
It is believed to yes, but in a number of galaxies have failed to detect a black hole astronomically. Indirectly "observation" the galactic central black hole, or its manifestations, are possible under two favorable situations :
-> For relatively close galaxies, where we can observe the movement of the glowing substance in their center - an enormously fast rotation around the central object, or the "silhouette" of the black hole.
-> In active galactic nuclei that produce strong collimated jets of fast particles and radiation from accretion disks, while absorbing large amounts of matter.
In many older galaxies, however, the central black holes have already absorbed everything in their vicinity, they have nothing to "eat" and no jet is produced. In such a case, the black hole is practically undetectable astronomically. However, it does not have to be a permanent condition. After a long enough time, perhaps thousands or millions of years, some star or a nebula may come into close proximity to the black hole, the black hole will begin to absorb it and create a new observable jet.
2."Does this supermassive black hole play a crucial role in the galaxy ?"
Here the answer is no! At least not now. The supermassive black hole at the center of the galaxy, as well as other black holes present, make up only a tiny fraction of the galaxy's total mass. They only add a negligible amount of gravity, nothing more. If we removed them all, almost nothing would change in the overall structure or dynamics of the galaxy.
The answer to these two questions evokes another tertiary question: "Why are black holes, when their mass is only a small percentage of the total mass of a large galaxy, usually found in the center of the galaxy?". In general, most black holes are not located in the central regions of galaxies, many smaller and medium-sized black holes are probably distributed in various places. But supermassive black holes are located in the center, which can basically have two alternative reasons :
- In the central part of the galaxy, there is the largest accumulation of stars and interstellar matter, so there are the best conditions for the formation of black holes and their growth to giant masses.
- Supermassive black holes were the seeds of large spiral galaxies. The galaxy thus formed around the black hole, which remained where it was before - in the central region.
However, if two galaxies collide, penetrate, and their central cores interact, the massive black holes may no longer remain at the center. In certain cases they may even be ejected away from the resulting merged galaxy..?..

Black-hole in binary systems
Let us now return to stellar black holes. Astronomical observations show that most stars are not isolated, but are part of a binary or multiple system - they are gravitationally bound and orbit (common center of gravity) - §4.2, passage "Binary stars and multiple systems". If two stars in a binary system do not orbit too closely around each other, they evolve independently, depending mainly on their mass. At a given time since their common origin, they could therefore reach various stages of their evolution. Either they can still be common stars of the main sequence, or one of them could already consume its thermonuclear fuel and shrink into a white dwarf or neutron star, or collapse into a black hole at high mass. For closely orbiting binary stars, the overflow of gases between the two components can be significantly applied (as discussed in the mentioned passage "Binary stars and multiple systems"). It can be expected that there will be a large number of binary systems in space, one component of which will be a black hole ...
In tight binary systems, in which one component is a black hole, the mass flowing from the other star around the black hole forms an accretion disk in which the gravitational binding energy (ie part of the mass) of the accreting mass is converted by dissipative processes into heat, which is radiated from the disk - Fig.4.26 (view in the direction of the axis of rotation) and Fig.4.31 (side view). The inner parts of the disk heat up to a high temperature and also emit X-rays. Due to instabilities and turbulence in the accretion disk, the emitted radiation has an irregularly variable intensity.

Fig.4.31
A close binary star system in which a stream of gas flows into a black hole orbiting a common center of gravity with an ordinary star, forming an accretion disk around the black hole. Narrow cones (jets) of radiation and ionized gas are emitted along the rotational axis of the accretion disk.

Note: This is an identical situation as in Fig.4.26, but observed "from the side", perpendicular to the axis of rotation of the accretion disk.

The best known example of such a system is the binary X-ray source Cygnus X-1, which according to astronomical observations consists of a blue giant star HDE 226 868 with a mass of about 25 M_¤ (distance from Earth about 2.5 kpc) and an optically invisible "guide" of at least ~6 M_¤ (this mass of the invisible component results from the Doppler measured velocity and period of the first component). The period of this eclipsing binary is 5.6 days. X-rays are irregularly variable with a characteristic period of the order of milliseconds, so that the dimensions of the emitting area are not larger than the order of hundreds of kilometers. The source of X-rays is the invisible guide, which cannot be a star, because at this mass an ordinary star would have a luminosity of ~10³ times higher than the Sun and would therefore be visible. This component cannot be neither white dwarf or neutron stars, because its weight significantly exceeds both Chandrasekhar, and Oppenheimer-Landau limit. So it is most likely a binary system of a normal star and a black hole according to Fig.4.26 or Fig.4.31, where a stream of matter flowing from a star to a black hole creates an accretion disk, in which the observed X-radiation are generated. Several similar "serious candidates" for the black hole are now observed, in addition to Cyg X-1, for example, the X-ray source Cir X-1, the binary star V861 Sco, or the object LMC X-3.
Even with a small blac holes from accretion disk along the rotation axis occurs jets of relativistic particles are ejected into the surrounding space (obr.4.31). Due to their geometric arrangement and some of their properties, the accretion disks around the black holes of stellar masses resemble much more massive distant quasars and radiation-active nuclei of galaxies, but as if reduced to much smaller scales - by a ratio of the order of 10⁶; therefore, these objects are sometimes called "microquasars" (compare Figs.4.30 and 4.31). A typical example of such an object observed in our galaxy is the binary source SS 433 with an orbital period of 13 days, whose secondary compact component has a mass of min. 5-10 M_¤ and emits from it, in addition to X-rays, two opposite gas jets at speeds up to 0.26c.
The above-mentioned apparently superluminal jet velocities were also registered in some microquasars whose jets were directed at a small angle relative to the observer. The first such case was the binary object GRS 1915+105 with a standard star and a black hole with an accretion disk.
Thus, in general, a black hole that forms a binary system with an ordinary star has the best chance of being proven. In the optical field in this binary system, we see only a star, which shows a Doppler spectral shift which periodically changes into red and blue regions as the star orbits its invisible companion approaches or moves away from the observer on Earth. From this measurement of the period and orbital velocity of the visible component, the mass of the second invisible component can be determined astronomically; if it is a compact object with a mass significantly larger than 2M_¤ and, in addition, X-rays or jets of relativistic particles come from there, it is probably a black hole.

Binary systems of gravitationally coupled black holes. Collisions and fusions of black holes and neutron stars .
From a mechanical point of view, black holes basically behave as very massive strongly gravitational bodies with relatively very small dimensions, which move evenly in a straight line in free space and move along curved geodetic paths in the gravitational fields of other objects. In vast outer space, there is a very small probability that two independent black holes would collide directly ("frontally") - it probably didn't happen anywhere during the entire existence of the universe. Even the mutual gravitational capture of two independent flying black holes is not very probable (they would have to encounter a low mutual velocity and a very small impact parameter, but see below "supermassive binary black holes"). The only real possibility of close mutual interaction ("collision" or fusion) of black holes is their common origin in a binary or multiple star system.
Binary systems of gravitationally coupled black holes (two or more) are undoubtedly very common in the universe, because they commonly form during the evolution of stars that are part of binary systems: when in such a binary (or multiple) system of massive stars (masses greater than about six times the Sun) at the end of their evolution, the gravitational collapse will occur to form compact objects. The mutual gravitational relation to the orbit will be preserved, so that the original binary system becomes a binary system of gravitationally bound compact objects, still orbiting the common center of gravity (we are mainly interested in the case where black holes formed by gravitational collapse). According to the laws of the general theory of relativity of a body in a binary system, gravitational waves radiate during their mutual circulation, carrying away part of the kinetic energy of the circulation - see §2.7, section "Sources of gravitational waves".
In most cases, the resulting black holes circulate at great distances.In conventional binary systems, the orbital distance is at least 10⁶ km (close "spectrometric" binary stars), which is more than 100,000 gravitational radii; at these distances, the GTR effects are practically not applied. During their circulation, only very weak gravitational waves (approx. 10²⁵ W) emit - the initial part of the graph in Fig.4.13. They would not reach the stage of close circulation by gravitational radiation during the entire existence of the universe! However, there is a mechanisms that can significantly "converge" in the foreseeable future: it's friction and acretion in a large and dense cloud of gas which, after collapse, often surrounds the binary system. If the two black holes approach each other at a distance of several tens of gravitational (Schwarzschild) radii, the intensity of the radiation of gravitational waves will increase significantly.
In this situation, the removal of the energy of the orbital motion by intense gravitational waves leads to the converging bodies approaching each other, shortening the orbital period, increasing the velocity of the circulation and increasing the frequency and intensity of the gravitational waves. This is shown in Fig.4.13-GW :

Fig.4.13-GW. Time course of amplitude, frequency and intensity of gravitational radiation of a binary system of two compact black holes m₁ and m₂ orbiting a common center of gravity.
Bodies that begin their orbit at time t = t₀ on some large radius r₀ descend very slowly in a spiral and continuously emit gravitational waves, initially weak (stage I). Even with tight binary systems, it is a process that lasts hundreds of thousands and millions of years. As you approach, the intensity and frequency of the radiation continue to increase. After reaching the circulation distance of several tens of gravitational radii, there is an avalanche-like increase in the intensity and frequency of gravitational waves (stage II). After reaching the limit innermost of stable orbit, the bodies fuse rapidly, sending a short intense flash of gravitational waves (stage III). In the upper part of the figure, enlarged sections from the last few cycles are symbolically drawn, during which both horizons are deformed and finally they are connected to the deformed horizon of the resulting black hole. The resulting black hole m₁+m₂ is rotating and rapidly relaxes to a stationary axially symmetrical configuration of the Kerr black hole (stage IV) by radiating damped gravitational waves.
Note: This figure is analogous to Fig.4.13 in §4.3 passage "Emission of gravitational waves during motion in the field of a black hole , related to the circulation of a body in the field of a black hole, but the qualitative character of the dependence is the same.

At first, the two components slowly, but with increasing speed, approach each other in a spiral and radiate more and more intensively by gravity (middle part of the graph in Fig.4.13). At the end of this avalanche-shaped "spiral of death", after a close approach, during the last few orbits and the subsequent merging of the two black holes, a massive flash of gravitational waves emits. Gravitational waves will carry about 5% of the total weight of both merging compact objects !
To summarize, the dynamics of the orbital binary system of black holes emitted by gravitational waves can be divided into 4 stages :
I.Distant orbital along almost Kepler orbits, with weak by gravitational radiation and very slow spiral approach. This phase can last several billion years.
II.After approaching a distance of several tens of gravitational radii, the intensity of gravitational radiation increases greatly, which leads to a rapid spiral approach of both bodies, with the emission of increasingly powerful gravitational waves with rapidly increasing frequency, from units to several hundred Hz.
In astrophysical jargon, this phase is sometimes called a "chirp" because the rapid growth rate of circulation just before the merger of two black holes resembles a bird chirp.
III.Fusion(merge, collision) of both black holes into one resulting rotating black hole, while is emitting a gigantic flash of gravitational waves.
IV.Relaxation of the resulting black hole on a stationary axially symmetric configuration of a Kerr black hole with a rapid attenuated reverberation of gravitational radiation.
In terms of the emission of gravitational waves, these processes are discussed in more detail in §2.7, section "Sources of gravitational waves".
More complex scenarios of collisions and fusion of black holes
From the point of view of black hole physics, we have so far assumed that a binary (or multiple) system of compact objects is "pure" - it does not contain any gas or other bodies. After the gravitational collapse, the resulting black holes around each other (around a common center of gravity) continue to orbit for millions of years at distances of several million kilometers - as a binary system of compact objects. At first, they have accretion disks from the remaining gases from the cloud around them (as analyzed above in the section "Accretion disks around black holes"), but gradually they "consume" them or discard them in the final stages of rapid circulation. In such an idealized case, the behavior of a "pure" binary system can be analyzed by the above scenario, in which only gravitational waves are emitted ( Fig.4.13-GW) .
However, during cataclysmic explosions of supernovae (and "hypernovae") in the final stages of massive stars, huge amounts of gases are ejected, some of which remain gravitationally bound in the source system. The binary system of collapsed stars is thus "immersed" in a dense cloud of gases, at least in the initial stage. If the binary system of two black holes is initially relatively tight, or friction in a dense gas cloud soon slows down the rotational speeds of both components, the final phase of aproching and merging will take place not in a vacuun, but in an environment with a high gas content. Perhaps there could be a larger and looser "common accretion disk" around a tight binary system..?.. In addition to the massive emission of gravitational waves, the collision-fusion of compact objects in such a system can also occur gas particles interacting with photon radiation, predominantly high-energy - a flash of gamma rays.
Another possible scenario is that it is a multiple system of two black holes and in addition a white dwarf or neutron star, which can supply a substance (gas) to the binary black hole system, which interacts with the emission of hard photon radiation during the collision..?..
In these more complex scenarios of black hole merging-collision dynamics, the massive emission of gravitational waves may be accompanied by a weaker emission of a flash of photon radiation .
Binary system supermassive black hole
Another way interaction and precipitation compact objects could be binary supermassive black hole at the center of galaxies (large black hole at the center of galaxies, the amount paid to the "quasars" passage "Mechanism of quasars and active nuclei of galaxies"). According to galactic astrophysics, they could form during galaxy collisions in situations where galaxies penetrate each other with a small impact parameter and at a lower mutual speed. Black holes in the center of both galaxies can then form a bound binary system as they "pass". Massive low-frequency gravitational waves would form as they circulate, gradually approach, and eventually fuse these giant black holes .
Collisions and fusion of neutron stars
After a supernova explosion, the neutron stars formed in the binary system also initially orbit at great distances (Fig.4.13 -FusionNeutronStars.). Relatively weak gravitational waves are emitted, carrying away the kinetic energy of the orbital motion (a). The neutron stars thus slowly approach each other in a spiral, the gravitational waves increase and the frequency increases, and the shape deforms during close orbit (b). Inevitably, finally they will "collide" and merge (c) - (the time for which this fusion occurs is given by the formula (2.82c) derived in §2.7, section "Sources of gravitational waves").

Fig.4.13 -FusionNeutronStars.
a) Two neutron stars orbiting in a binary system at a great distance descend very slowly in a spiral and continuously emit gravitational waves, initially faint. b) As you approach, the intensity and frequency of gravitational radiation continue to increase. c) During a close approach, deformation occurs and eventually a collision and fusion of the two neutron stars occurs. d) With rapid rotation during fusion, a large amount of neutron substance can be ejected, which immediately nucleonizes to form predominantly heavy nuclei, followed by radioactive decay. e) The resulting object, after the instabilities subside, is either a neutron star or a black hole (according to the remaining mass). This resulting object will have only a small accretion disk around it (since most of the substance has been ejected away by the enormous energy released during explosive nucleonization).

During a rotational collision (c) and the merging of two neutron stars (or a neutron star with a black hole) in a binary system, their elliptical deformation occurs, during which a large amount of neutron material (d) is ejected by centrifugal forces. As soon as this neutron substance breaks out of the grip of the massive gravity of the neutron star, it becomes highly unstable and immediately explodes - rapid decompression from a nuclear density of 10¹⁴g /cm³. Neutrons with weak interaction are promptly transformed into protons: n^o ® p⁺ + e^- + n (cf. "Radioactivity beta^-" in the treatise "Radioactivity" in the monograph "Nuclear Physics, ionizing radiation"). The dense mixture of protons and neutrons due to the strong interaction occurs immediately "nucleonization" - thrown material is converted to the nucleus of heavy elements (in a manner similar r- process in supernova), which is accompanied by explosion and gamma-ray bursts. This heavy nuclei is then already more slowly radioactively converted into the nucleus of other heavy elements and glow intensely with longer afterglow. This process can enrich the surrounding universe with heavy elements, similar to the previous supernova explosion (which formed the participating neutron stars a long time ago). The resulting substance (in the plasma state) is ejected into the surrounding space mainly in the opposite cones along the rotational axis of the system.
Collision-fusion of two white dwarfs or neutron stars (or neutron stars with a black hole) thus, besides gravitational waves, accompanied by a strong optical astronomical effect - emission of intense flash energy photon radiation, short GRB, with a gradual fading through gamma from radioactivity, UV radiation, visible light, to radio waves.
*)Such an astronomically observed event is sometimes called a "kilonova" - it can be up to 1000-times more powerful than a normal nova, especially if observed from the direction of the binary system's rotation axis. Neutron star fusion, however, is a completely different process that has nothing to do with a nova explosion. Although the name kilonova is misleading, in the astronomical literature it has become...
What final object obtained after merging of a binary system of neutron stars (after recovery from transient instabilities )? This probably depends mainly on the total weight of the system. When two massive neutron stars merge, a "supermassive" neutron star is likely to form initially, which will be unstable and quickly collapse into a black hole. The fusion of two lighter neutron stars should result in the formation of a neutron star. The type and weight of the resulting object will also depend on the rotational angular momentum and the amount of ejected substance. For more massive binary systems, there will be a rapid collapse, so it will be sufficient to create less ejected neutron masses. If the initial mass is low, a resultant long-surviving or stable neutron star can be formed with more ejected material, which can radiate more intensely and for a long time. So we can expect roughly inverse relationship between photon emissivity (amount of radiation emitted in the process) and the initial weight of the binary system.
In most cases, the collision of ordinary neutron stars is expected to result in an explosion accompanied by jets of radiation at various wavelengths ("kilonova"). However, when somewhat more massive neutron stars collide, they can almost immediately collapse into a black hole, which quickly eats up almost all of the mass of both neutron stars. Almost no radiation escapes then from the collision site - the kilonova is not observed...
This process of collision and fusion of intermediate mass neutron stars was recently observed for the first time by detecting gravitational waves and at the same time electromagnetic waves - §2.7, passage GW170817. This is "good news" in terms of the diversity of the chemical evolution of the universe: as this fusion of neutron stars occurs more frequently, a significant number of heavy elements are continuously formed. And it will continue to be formed in the distant future - even decades and hundreds of billions of years, when no more active stars will shine and no supernovae explode in space (see §5.5 "The future of the universe"), pairs of neutron stars will still collide and form hot-matter districts rich in heavier elements. Perphas there will be something to develop from life and create other complex structures..?..
How many heavy elements in the universe are formed by collisions and fusions of neutron stars ?
The mechanism of nucleonization of the ejected neutron substance represents an "additional" formation of heavier elements from the substance, which would otherwise be lost due to the chemical evolution of the universe, would remain permanently gravitationally trapped in the neutron star. From the point of view of the chemical evolution of the universe, it is important how much matter, formed by heavy elements, is formed during the collisions and fusion of neutron stars. Nuclear-astrophysical analyzes show that when two neutron stars of usual masses of about 1.2-2 M_¤ merge, the amount of ejected neutron matter is estimated to be about 0.1 M_¤. Its nucleonization could create about 0.05 M_¤ (=~16000M_Earth) elements heavier than iron - of which about 5M_Earth elements from the lanthanide region, about 10M_Earth elements around gold and platinum and about 2M_Earth heaviest elements around uranium.
To assess the extent to which neutron star fusion contributes to the overall cosmic nucleogenesis of heavier elements - along with stellar synthesis and supernova explosions (cf. §4.1, 4 "Evolution of stars" and §4.2, "Astrophysical significance of supernovae") - it is necessary to estimate how frequent these events of neutron star fusion in space are. The initial astronomical data here is the number (percentage) of close massive binary stars with masses of 2÷8 M_¤, which explode as supernovae at the end of their lives and lead to the formation of neutron stars. These neutron stars then orbit each other, emit gravitational waves, and after a time given by the formula (2.82c) - ranging from about 100 million to more than 10 billion years - combine to eject a portion of the neutron mass that nucleonizes to form heavy elements (as mentioned above). The frequency of occurrence of this neutron star fusion event is estimated at (200 - 1000) Gpc^-3year^-1 (perhaps in the space of one cubic gigaparsec, max. a thousand neutron star fusions per year ...) *).
*) The great uncertainty of the expected frequency of neutron star fusion is due to the fact that we do not know well enough the initial parameters of neutron star orbits in the binary system, nor the density of possible braking gaseous medium in which neutron stars orbit. If the circulation took place in a vacuum, the frequency of occurrence would be even lower.
The resulting analyzes show that the fusion of neutron stars does not occur often enough to explain globally *) most of the observed amount of heavy elements in space. It is an important component, but the main source of heavy elements is probably stellar nucleosynthesis and supernova explosions (as discussed in §4.2, section "Astrophysical significance of supernovae"), including high-performance fast-rotating supernovae with a strong magnetic field.
*)Locally, however, it can be an important resource. If neutron stars collide and fuse in the vicinity of several hundred light-years from the germinal gas-dust nebula from which protostars and then stars form, the emerging stars and the planetary systems around them can be enriched with heavy elements, more than stars in areas where this process did not occur. Nuclear-analytical methods of studying the content of isotopes in meteorites suggest that something like this happened even before the formation of our solar system ...
Gravitational "Standard Siren"
The detection of gravitational waves from the fusion of neutron stars, together with the simultaneous detection of electromagnetic radiation from their optical counterparts, also has astrophysical-cosmological significance for the independent determination of the distance of the respective objects. This measurement makes it possible to combine the determination of the distance to the source derived from the gravitational wave analysis with the receding velocity derived from the redshift measurement using electromagnetic signal spectrometry. This approach not requires the use of a cosmic distance "ladder" (discussed in §4.1, passage "Determining the distance of cosmic objects - a fundamental condition of astrophysics"). The analysis of gravitational + electromagnetic waves can thus be a measurement of the direct determination of the relationship distance <--> luminosity in cosmological scales, without the use of intermediate distances, with sometimes problematic continuity. Gravitational wave detection is therefore sometimes metaphorically referred to as a "standard siren" - a gravitational-wave analogue of the electromagnetic "standard candle" (cepheids, Ia supernovae) used to determine large cosmological distances...

Influence of black holes on the surrounding universe
From the general-relativistic theory of black holes, presented in §4.2-4.7 (in connection to §3.4-3.6), it might seem that :
n 1. Black holes are locally very effective "vacuum cleaners" of matter from space - "bottomless abysses" into which matter falls and disappears irretrievably from space;
n 2. However, black holes have, due to their compactness, a very small "radius of action" compared to cosmic scales.
However, the properties of rotating accretion disks around black holes change these conclusions somewhat :
¨ ad 1. Not all matter that gets close to a black hole is irretrievably lost. If the black hole rotates rapidly, then a relatively large portion of the hot gas descending in the vortex of the accretion disk can be ejected in a pair of jets along the axis of rotation. With rapidly rotating black holes, up to 25% of the mass that enters the accretion can be ejected.
¨ ad 2. The jets of matter and radiation along the rotational axis of the accretion disks of supermassive black holes extend to great distances of many hundreds of thousand light-years (as seen, for example, in Fig. 4.29), where they can affect the dynamics of star formation and galaxy evolution. The effective range of black holes - their "radius of action" - thus increases sharply.
Black holes surrounded by an accretion disk are no longer just small but bottomless and mysterious "holes in space", but they become dynamic objects, contributing significantly to the dramatic events observed in outer space. Overall, we can say that black holes already have an important place in astrophysics, and so far all indications are that the importance of black holes in the further development of knowledge of the structure and evolution of the universe will continue to grow.

"Holes" in space
Contemporary relativistic astrophysics has come up with the concept of four types of "holes" - deep defects in the structure of spacetime that could, at least theoretically within GTR, exist in space :
¨ Black holes ,
representing an area in which attractive gravity is so strong, that they do not "let" even light out - a horizon of events will form around this area. Typical black holes are formed by the gravitational collapse of sufficiently massive stars (§4.2 "The final stages of stellar evolution. Gravitational collapse. The formation of a black hole."), they are a kind of "posthumous" remnants. We have dealt with the theory of black holes extensively throughout the existing chapter 4 " Black Holes ".
¨ White holes (hypothetical) ,
which are a certain "opposite" of black holes. Radiation and matter fly out of the white hole area into the surrounding space. In §4.4 "Rotating and Electrically Charged Kerr-Newman Black Holes", we showed the theoretical possibility of how inside a rotating black hole, matter below the inner horizon could "miss" the singularity and emerge in another region of space-time - in "another universe"; this place would appear here as a "white hole". At the same time, we subjected this possibility to a critical analysis, which revealed a de facto impossibility this process. Thus, there are no theoretical or observational indications for white holes of this kind. However, the final phase of quantum evaporation of a hypothetical black "micro-holes" could appear as a white hole (§4.7 "Quantum radiation and thermodynamics of black holes").
¨ Gray holes ,
which would be a kind of "transition state" between the absorbing black hole and the radiating white hole. According to quantum gravity, every black hole would in fact be "gray" - on the one hand it would irreversibly absorb matter and radiation, but on the other hand it would quantumly emit other radiation (§4.7 "Quantum radiation and the thermodynamics of black holes ").
¨ Wormholes (hypothetical) ,
representing a kind of "topological shortcuts" in space through which the particles can pass through and overcome huge spatial distance between distant places in the universe, or even penetrate into the "other universes" (discussed in §4.4, passage "Wormholes").

Gravity, black holes and space-time physics :
Gravity in physics	General theory of relativity	Geometry and topology
Black holes	Relativistic cosmology	Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy


4.7. Quantum radiation and thermodynamics of black holes		4.9.Gravitational collapse - - the biggest catastrophe in nature

What is the role of black holes in the universe?