Chapter 4
BLACK
HOLES
4.1. The
role of gravity in the formation and evolution of stars
4.2. The
final stages of stellar evolution.
Gravitational collapse 4.3.
Schwarzschild static black holes
4.4. Rotating
and electrically charged Kerr-Newman black holes
4.5. The
"black hole has no hair" theorem
4.6. Laws
of black hole dynamics
4.7. Quantum
radiation and thermodynamics of black holes
4.8. Astrophysical significance of black holes
4.9. Total
gravitational collapse - the biggest catastrophe in nature
4.8. 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 role
do these
black holes play in space?
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, paragraph " There are "complete"
black holes in space? ").
Opinions on the role of black
holes in space have changed radically in the second half of the 20th centaury. 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 nonsense"!) . After the discovery of quasars - see note below *) and pulsarsthis 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...
Now that 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 special 3C48 radio source 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 faint bluish telescope in
the Palomar 5-meter telescope a 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 10 6 -10 8 years. The source of
the jets must therefore bea very massive rotating
structure , the 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...
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. 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 will form,
and a black hole will form. 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 momentum was radiated by the gravitational waves did the
collapse and the formation of the resulting rotating black hole be
completed. Thus, black holes of stellar masses M ~ (1 ¸ 100) M¤ can originated
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 M ¤ ; lighter stars end their existence
mostly like neutron stars or
white dwarfs (due to large weight losses at the end of
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. 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" will
limit and they experience inelastic collisions and
interactions, leading to the
merging of
some stars in compact units. They can be formed, and gradually
increase supermassive objects that can easily become so thick
that it collapses into a giant black holes from weights from ~ 10 2
-10 4 M ¤ (in clusters) to 10 ~ 9
M ¤ (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 (another
possibility of supermassive black holes in the center of galaxies
is mentioned below at the end of " Thick accretion
disks. ") . 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
for black holes in stellar masses and supermassive black holes in
the cores of galaxies. The medium-mass black holes (~ 10 2 -10 4 M ¤ ) expected in star
clusters have not
yet been observed.
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 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 masterpiece. 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. |
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Right : Two massive jets (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 10 15 M ¤ ) of observed supermassive black holes in
the center of galaxies (see below " Mechanism of quasars and active
nuclei of galaxies " ) . For very small primo r diálních
black holes would in turn prevailquantum
evaporation (see §4.7 " Quantum
radiation and thermodynamics of black holes ") ;
all primordial black holes weighing less than about 10 15 g would have to evaporate completely to
this day *). The final phase of quantum evaporation takes place
in the form of a massive explosion, during which a large amount
of energy is released in the form of a flash of predominantly
hard radiation g . For the existence of primordial
black miniděr are not yet any direct or indirect evidence
(observation trying to register the appropriate hard gamma bursts
were unsuccessful), so their astrophysical significance was not
discussed.
*) With the Hawking effect, in a vacuum every black hole of mass
M evaporates completely in about T @ 10 65 .
(M / M ¤ )3 years.
Small and medium
primordial black holes are sometimes considered as one of the
suitable "candidates" for hidden
(dark) matter in galaxies and clusters of
galaxies (§5.6, passage " The future evolution of the
universe. Hidden-dark matter.
") .
Virtual black holes?
As part of attempts at the quantum theory of gravity
, a 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 -43 seconds ( Planck's time).). Virtual black
microdires 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 ") .
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, 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 rotation of the black hole and the
similarly.
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 vacuum the dust perfectly (and
pull out the carpet fabric), but only in the millimeter
environment ...
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" black hole with time increases
by two mechanisms :
- Growth in the size of the black hole (the horizon) as a
result of accretion of matter.
- Emission of gravitational waves each
gravitationally bound system of the circulation of 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 (~ 10 35 years), 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): E1wave = m - Ems , 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 correcting
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 E2wave @ 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 = E 2
wave
, while a body descending gradually along a spiral radiates
significantly more energy: Ewave ~ E1waves + E2wave . 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. Precipitation 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
below the horizon (where there are only 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
) *), in which a
black hole absorbs the surrounding material and thus
increases its weight. The surrounding substance, especially gas,
is drawn in by a massive gravitational field and when it falls on
a black hole , it is heated to such a high temperature that
it occurs due to strong adiabatic compression and braking by
viscous friction (this is also caused by turbulence, shock waves, etc.). to strong emission of not only infrared
and visible light, but also X-rays. During accretion, an
otherwise non-radiant black hole becomes a brightly
lit object
! More precisely, the glowing object is the absorbed
gas in its
vicinity.
*) 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.
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 is dM A/ dt (which is the amount of gas
absorbed per unit time) 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 may not 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
momentum - significantly larger than it
corresponds to
circular orbits near the horizon. In this case, the gas absorbed
around the black hole creates a rotating disc-like formation
called an accretion disk - a cloud of gas that swirls and
sinks into tha black hole. In this accretion
disk, the gas revolves around a black hole,
is braked by viscous friction 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 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.
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 :
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Fig.4.27. When accreting a gas with a specific 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. |
The gas particles in the
accretion disk move approximately in circular geodetic orbits. In
the inner orbits, the gas particles move faster than in 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 momentum is transferred from the inner part to the outer
part of the disk. The inner particles thus fall 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.
Thus, due to the viscous friction *) on the outer layers, the gas
particles in the inner layers are thus inhibited, 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 apply, because (similarly to spherical accretion) the
quadrupole moment does not change with time. In this process, there is a current of
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
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
precipitation of large 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.
Under the circumstances common in our
terrestrial conditions, friction is not exactly a 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 huge gravitational energy, substantially greater than the
nuclear energy. Therefore, friction effectively heats the disk so
much that it can glow more than 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
W = ( 1 - ` E ms ) .c 2 . dM A / dt , | (4.66) |
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 mass into the radiated energy is thus given by the
specific binding energy 1-` E ms of 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 momentum of the absorbed mass *). Change of
mass and 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 rotated by the theoretically up to the extreme state J = M
2 (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 M 2 [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 momentum of the accretion
disk is sometimes called canonical .
*) The gas falling in a spiral into a black
hole brings momentum and spins it at
ever-increasing speeds. When the black hole is about twice its
weight by this absorption, it reaches an 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 GMc /O ( » 1,3.1031 M / M ¤ [J.s -1 ] (where opacity O
caused by classical Thomson scattering of 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 "thicken". 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.
One of the
possibilities of determining the rotational speed of an accretion
disk is spectrometry . The spectral lines of gas
radiation from the inner part of the rotating accretion disk are
significantly widened by the Doppler effect fast orbital
motion (thermal expansion of spectral lines caused by chaotic
motion of individual gas particles is in this case much smaller
than Doppler expansion by fast ordered motion in the accretion
disk). In addition, the fundamental energy of the photons is reduced
by the gravitational redshift relative to the known
laboratory energy. At high rotational speeds, the spectral lines
of the accretion disk should 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 (due to relativistic effects the two local maxima
will have slightly different heights, also depending on the slope
of the disk with respect to the direction of the observer).
Radiation from the inner part of the accretion disk occurs mainly
in the X-ray spectral region. Astronomical X-ray spectrometry
is still in its infancy. However, future sensitive spectrometers
located on space probes will certainly be able to measure fine
details in the 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.
At origin jets
from the accretion
disk of a rotating black hole probably also play an important
role magnetic field *), whose 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. 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
cloudshigh-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.
*) Magnetic extraction of black hole rotational
energy
In addition, a very strong magnetic field in the central part of
the accretion disk (which could reach up to 10 10 T) 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,
it creates a strong poloidal magnetic field by rotating toroidal
currents flowing in the equatorial plane. The entrainment of
space and magnetic field lines by the rotation of a black hole
then induces a powerful electric generator 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, which can reach up to 30%
(from mc 2
) * for fast-rotating black holes, can only be envied by existing
jet or rocket engines! "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 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 (obr.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 it brightens all the other stars in the galaxy with its
brightness of 100-x and 1000-x. 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 disksgoes
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, 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
-109 M¤ . 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 side 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 to the field of view .
*) 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 luminous dot 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.
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
~106-9 M¤ ) , 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; 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
"moment" a quasar or an active
galactic nucleus is formed again .
*) 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 > ~ 1011 M ¤ 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, lighter 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 ", paragraph " 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 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
options (in descending order are the
opposite direction of the timeline) :
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.
*) 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 cloud of dense gas
(and dark matter..?..) in the center of the emerging galaxy could collapse
directly into a large black hole ,
without the need for star formation and evolution - without
collapse into black holes of stellar masses.
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 ..?..
It is probable that the gravitational collapse of large
gas-dust clouds and possibly the connection of the resulting
black holes significantly contributed hidden- dark matter
(its existence and properties are discussed
in §5.6, section " Future evolution of the
universe. Hidden-dark matter.
") , whose attractive gravitational
effects prevailed over repulsive presure forces in large
contracting gas clouds ..?..
Many observed quasars are very old,
probably formed about 200 million years after the beginning of
the universe. So far, we are not able to convincingly explain how
such gigantic black holes could have formed so soon
after the beginning of the era of substance..?..
Black-hole
binary systems
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 over 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 ~ 10 3 times higher than the Sun and
would therefore be visible. This component can be neither white
trpasl s brush 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 holes of small black accretion
disk along the rotation axis occurs jets of
relativistic particles to 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 10 6; 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. 5-10M ¤ and emits from it, in addition to X-rays, two opposite
gas jets at speeds up to 0.26c.
Thus, in general, a black hole
that forms a binary system with an ordinary star has the best chance of proof , because the mass and second
velocity of the visible component can be used to astronomically
determine the mass of the second invisible component; in the case
of a compact object weighing significantly more than 2M¤ and moreover, X-rays or jets of
relativistic particles come from here, it is probably a black
hole.
Binary systems of gravitationally coupled
black holes. Precipitation and fusion of black holes and neutron
stars .
From a mechanical point of view, black holes basically behave as
very massive strongly gravitational
bodies and
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") - probably
not anywhere in the life 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) ) will
occur at the end of their evolution gravitational
collapse 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 :
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Fig.4.13-GW.
Time course of amplitude, frequency and intensity of
gravitational radiation of a binary system of two compact
black holes m 1 and m 2 orbiting a
common center of gravity. Bodies that begin their orbit at time t = t 0 on some large radius r 0 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 +m 2 is rotating andrapidlyrelaxes 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 parlance, 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
(fusion, collision) of both black holes into one resulting
rotating black hole, 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 and quasars 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 (b) deforms during close orbit .
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) During 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 disappear, 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 1014 g /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.
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 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 ..
This process of collision and fusion of
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¤ (=~16000MEarth)
elements heavier than iron - of which about 5MEarth
elements from the lanthanide region, about 10MEarth
elements around gold and platinum and about 2MEarth
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 ...
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"
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
").
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4.7. Quantum radiation and thermodynamics of black holes |
4.9.Gravitational collapse - - the biggest catastrophe in nature |
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 |