Catastrophic gravitational collapse into a black hole

Chapter 4
B L A C K     H O L E S
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

4.9. Total gravitational collapse - the greatest catastrophe in nature and the deepest paradox in physics

Let's think, at the end of this Chapter 4 on black holes, about some general aspects of the phenomenon of gravitational collapse. We can distinguish three areas or levels of gravitational collapse :

Level 1 - collapse of stars
In §4.2 "The Final Phases of Stellar Evolution. Gravitational Collapse. Formation of a Black Hole." we have analyzed in detail how, at the end of their evolution, after the end of thermonuclear reactions, stars shrink or collapse rapidly under gravity to form a white dwarf, a neutron star or a black hole - depending on their remaining mass.
   The apocalyptic picture of the gravitational collapse and the formation of a black hole, which we have discussed in this chapter, generally shows that any sufficiently massive system that "fails" to get rid of excess matter~energy during its evolution, according to general theory of relativity, is doomed to the fate of the black hole.
   For very massive systems, this does not even require any "exotic" conditions of a white dwarf or a neutron star, where it can be argued that we know relatively little about the behavior of matter under such conditions. For example, a formation (a cluster of gas and dust or a giant star) with a mass of the order of 10⁸ M_¤ reaches its gravitational radius (which is several hundred thousand kilometers) and creates a black hole at a density of only the order of grams/cm³, which is the density we are used to from terrestrial scales, so we cannot expect any unknown anti-shrinkage effects here. In such a case, it is not even enough to ignite thermonuclear reactions before the horizon.
   Or another example. Let us have a galaxy composed only of stars (let's say there are ~10¹⁰) moving in a common gravitational field. Imagine that in an imaginary experiment, we changed the velocities of all the stars to move only toward the center, whereas this center of galaxy would reach at about the same time. This would be possible in principle, because that the energy needed for this is small compared to the total mass ~ energy of the stars. In principle, this can be done so that the area around the center, in which the stars thus gather, is, for example, 10 times larger than the solar system. There is enough space in this volume for all the stars, so that with the appropriate "direction" of their movement, collisions can be avoided. If we compare the sum of the masses of all the stars with the dimensions of the region in which they are concentrated, we find that the stars are located inside the Schwarzschild sphere. In this rather innocent-looking process with ordinary stars (without any catastrophic events) thus a horizon of events was formed - a giant black hole was created! The stars, which would otherwise be able to avoid collisions, will then actually be drawn into the center, and there they will all collide into singularity; according to Theorem 3.4, a singularity is created, because the light rays diverging from the center will be bent and focused as they pass the individual stars and begin to converge (a closed trapped surface appears - §3.3).
   The described examples show that the formation of a black hole generally does not depend on any not sufficiently substantiated assumptions about the behavior of matter under extreme conditions. The only assumption is the validity of the general theory of relativity, especially the complete universality of gravity in every situation.

Level 2 - collapse of the universe
In cosmology, it turns out (Chapter 5 "Relativistic Cosmology") that the gravitational collapse of a star is a certain analogue (sometimes even figuratively called a "laboratory sample") of a hypothetical phenomenon even more grandiose - the collapse of the whole universe. If the average density of matter in the universe is sufficiently high, predicts relativistic cosmology closed universe: current expansion is once stopped and will be replaced shrinkage (collapse). This close analogy between the gravitational collapse of a star and the collapse of the entire universe (or the time-reversed "big bang") can help better understand these cosmological problems. The gravitational collapse of a star is a much simpler phenomenon than the cosmological problem of the evolution of the whole universe - it is a local phenomenon, so it is not necessary to know the global structure of the whole universe for its analysis *).
*) If we take the position opposite to Mach's principle. However, even if the local laws of physics were strongly influenced by the structure of the universe as a whole (as would follow from Mach's principle - Chapter A "Mach's Principle and General Theory of Relativity"), such a local event can be expected to be far less "sensitive" on the global structure of the universe than the cosmological problems of the evolution of the whole universe (but see also the conclusion of §4.4, section "Black holes - bridges to other universes?", passage "Black holes - "hatcheries" of new universes?').
   In terms of the fate of the observer, however, between these two kinds of collapse (the stars and the entire universe) is a fundamental difference. When collapsing star has observer in principle is always a choice: either to remain at a safe distance and see only part of the collapse to the horizon, or falls under the collapsing matter and see the whole course of collapse to a singularity, but in no way will not be able to communicate their findings out and will inevitably be destroyed (at least as regards the collapse of the non-rotating uncharged star in the classical case). When the collapse of the entire universe the observer no longer has this choice - he cannot avoid the fate of all other matter, the collapse of the universe will be universal.
   In terms of objectivity, however, it should be noted that this is only a hypothetical situation that will not occur in space! On the contrary, current cosmology in co-production with astronomical observations shows, that the universe is probably open and will expand, even with accelerated speed (§5.6 "The Future of the Universe. Arrow of Time. Dark Matter. Dark Energy", part of "Accelerated Expansion of the Universe? Dark Energy?")...

Level 3 - quantum collapse
The third level of gravitational collapse can be expected on the contrary in the microworld. In quantum geometrodynamics (see §B.4 " Quantum geometrodynamics ", Fig.B.6) it is assumed that processes similar to gravitational collapse (but reversible) take place everywhere and constantly on scales of the order of ~10^-33 cm in the form of quantum fluctuations in geometry and topology of space - space-time has a "foamy" constantly fluctuating microstructure (see also below passage "Monstrous singularity").

Can a black hole engulf us and the whole universe ?
The short and most likely answer is succinctly: it can't ! In order to justify why probably not and under what circumstances perhaps yes, let's have a brief discussion of the individual options.
   From the astronomical point of view, black holes of stellar masses have small dimensions of the order of kilometers, so their "radius of action" is completely negligible on cosmic scales (it was discussed in §4.8, passage "Limited "radius of action" of black holes "). Of course, such a black hole cannot engulf the universe, or the galaxy or the star cluster. However, it can destroy and partially engulf the individual stars it encounters. A "stray" black hole that would hit Earth would, of course, destroy us and engulf us. However, the probability of such a collision is very small.
   Giant black holes with masses of a few million M_¤, probably located in the center of most galaxies, but they do have much greater "radius" than stellar black holes. But what are those 10 million kilometers (or 10 light-seconds) compared to the galaxy's diameter of about 200,000 light-years?! Thus, there is also no immediate danger of the whole galaxy (and with it our Earth) being absorbed by its central black hole. However, in a very long time about 10²⁰ years, the galaxy will perhaps eventually collapse into a giant black hole - due to the friction of interstellar gas and the emission of gravitational waves carrying away rotational energy. In such a long time, the shape of the orbit of our solar system around the center of the Galaxy is likely to change significantly due to the gravitational action of many massive stars and their clusters that the Sun will encounter. Therefore, it may happen that our Earth will eventually end up in a black hole in the middle of the galaxy... - or, conversely, it may be ejected out of the Galaxy..?.. However, all this would happen only after an extremely long time, during which humanity will have to face many other catastrophes and when the Earth, the Sun and the solar system will no longer exist..!..
   The various possibilities for the evolution of galaxies and the entire universe in the extremely distant future are discussed in §5.6 "The Future of the Universe. The Arrow of Time. Hidden Matter. Daek energy.".
   Black microholes have only a tiny gravitational "radius of action" and can practically not absorb anything macroscopic. However, they could endanger us with their radiation during their quantum evaporation by the Hawking mechanism (§4.7 "Quantum radiation and thermodynamics of black holes"). However, no black microholes have been found yet, and even if they did exist, their "close encounter" with Earth would be extremely unlikely ...

Catastrophic gravitational collapse !
Not only matter, but also time and space fall into a bottomless abyss with the gravitational collapse. At the "bottom" of this abyss, mass is destroyed in the region of infinite curvature of spacetime. Here, each object is transformed into a stream of subatomic particles. During the gravitational collapse (especially in the final stage in the vicinity of the singularities) leads to disruption of both molecules and atoms collapsing mass, but also to the destruction of the nuclei themselves, and even elementary particles. The gravitational collapse into a black hole represents the definitive "victory of gravity over matter", in which matter irreversibly loses its material nature.
   Therefore, the gravitational collapse and formation of a black hole can rightly be declared the most catastrophic phenomenon in nature, which most deeply degrade and destroys matter. According to the "black hole has no hair" theorem (see §4.5) when gravitational collapse they erase all individual characteristics of matter and remain only the common basis: total mass, electric charge and rotational angular momentum. Disappear without a trace even those characteristics which in all other phenomena in nature preserve (e.g. baryon charge, informations). It can be said that  all other catastrophic phenomena, including the explosion of an atomic or hydrogen bomb and even the annihilation of matter and antimatter, are just pranks compared to a complete gravitational collapse !
   When astrophysicists recognized of the unusual phenomena that gravitational collapse could lead to, they looked for "a law of physics that would prevent stars from doing such nonsense" (Eddington). It turned out that such a law probably does not exist, and now the consequences of the gravitational collapse for the outside observer are almost universally accepted.

Irreversibility and loss of information
In classical physics (mechanics, electrodynamics) as well as in quantum physics, all known phenomena are reversible: at least in principle we could be able to reverse the motion of all particles and regain the previous state. However, the complete gravitational collapse into a black hole is, in principle, an irreversible process. From below the event horizon, no particle can get back. Closely related to this irreversibility is a problem called the information loss paradox : a black hole destroys information about absorbed particles, that would allow us, at least in principle, to reconstruct their backward movement (discussed in §4.5 "Black hole has no hair" and §4.7, passage "Quantum evaporation: mass return and information from a black hole?"). It turns out that the loss of information below the horizon is not a paradox, but the physical reality: the laws of space-time "boss" also informations !

Monstrous singularities
But what about singularities inside a black hole? *) At one time it was hoped that the singularity in solving gravitational equations is only a consequence of the assumptions about exact symmetry and that a violation of symmetry (or rotation) could perhaps prevent singularities. However, the general research of Penrose and Hawking (see §3.8) shows that singularities in solutions of equations of classical GTR naturally occur under very general assumptions, which are probably fulfilled in practice.
*) The existence of a singularity inside a black hole is discussed in §4.2, section "External and internal view of gravitational collapse" and in the passage "What is inside black holes?" at the end of §4.2. Properties of singularities are analyzed in §3.7 "Spatio-temporal singularities" and §3.8 "Hawking's and Penrose's theorems on singularities".
   However, singularity is something absurd that physics can hardly come to terms with: in singularity the existence of every object that gets there ends, no physical laws apply there. For the outside observer, everything is all right - for it only after an infinite time will horizon arises, and therefore never singularity. However, the collapsing matter itself will inevitably in its finite time reaches a singularity - the point where "ends physical world"! Gravitational collapse is thus also the biggest paradox in contemporary physics, as emphasized by J.A.Wheeler [181]. This can be compared to the well-known paradox of the electrical collapse of an atom, which arose in the first decade of the 20th century after elucidating the basic structure of atoms in the application of classical electrodynamics, according to which such a composite mass would collapse electrically in a fraction of a second (~10^-10 s), in stark contrast to reality. This paradox was eliminated by N.Bohr with his three postulates (§1.1 "Atoms and atomic nuclei", passage "Bohr's model of the atom" in the monograph "Nuclear physics and physics of ionizing radiation"), which was then explained by quantum mechanics. There is therefore some hope that the paradox of the gravitational collapse to singularity will somehow be resolved in the future on the basis of a consistent quantum theory of gravity (cf. the discussion in §B.4 "Quantum Geometrodynamics").
   In close proximity to singularities, in the picoscales of quantum geometrodynamics, quantum gravity begins to play an important role, which significantly changes the basic concept of spacetime of the theory of relativity. Quantum fluctuations of spacetime curvature become so huge here that they completely deform all objects and disrupt the continuity of time. The relativistic unification of space and time is separated here. Time ceases to exist - it is no longer possible to distinguish whether one event took place before another event, the terms "before" and "after" no longer exist. Causality is "canceled" here. Space, separated from the original spacetime, is unrecognizably deformed and ambiguous, becoming a prank of chaotic quantum fluctuations. It is no longer possible to distinguish what is to the right or left, closer or farther. Figuratively, "monstrous singularity dissolves in bizarre quantum foam" - compare Fig.B.6 in §B.4 "Quantum geometrodynamics". Hard to say which is better..?..
   There were also been hopes, that singularities could be prevented by the hypothetical assumption that spacetime does not have a smooth continuous structure, but on very small scales spacetime is quantized - it has a discrete structure (§B.5, passage "Discrete structure of spacetime"). It consists of a huge number of very small, already indivisible elementary "cells". This hypothetical "quantum geometry" could perhaps have a magnitude of the order of the Planck length of 10-³³cm. In such a case, the gravitational collapse inside the black hole would not continue until the zero-size singularity, but would stop after reaching a certain minimum size structure, since the elementary cells of space can no longer be compressed to anything smaller...
   This generally possible acceptable hypothesis of a quantum discrete space-time was followed by some already purely speculative scenarios proposed by some supporters of the loop theory of gravity (it is also mentioned in the conclusion of §B.5): that after the collapse to the smallest possible size there would be a kind of "quantum rebound" and contraction would go into expansion - the black hole would explode and turn into a white hole. These speculations are not supported by any real astrophysical findings...
   Perhaps an astrophysically more plausible scenario for the formation of white holes is the formation of a topological tunnel instead of a singularity - a "worm hole", through which the collapsed matter can pass and fly out the opposite mouth of the tunnel in another place, which then appears as a "white hole". Even here, however, there are unresolved problematic aspects (§4.4, passage "Black holes - bridges to other universes? Time machines?").
 Gravastar ?
One of the last recent attempts to eliminate the difficulties of the final state during gravitational collapse is the hypothesis of a "gravitationally condensed star" called a gravastar (gravitation vacuum star), which was proposed in 2001 by the American astrophysicists P.O.Mazur and E.Mottola. It is an alternative to black holes. From the outside, it appears similar to a black hole: in the centrally symmetric non-rotating approximation, a gravastar is a spherical object that has a regular Schwarzschild spacetime geometry in outer space. Inside, however, spacetime has a de Sitter geometry, i.e. the interior is filled with dark energy (with equation of state p = -r), whose antigravity effects prevent it from collapsing into a singularity. It does not have an event horizon, but the outer and inner regions are separated by a thin layer of extremely dense matter (with equation of state p = r), which represents the mass of the star from which the object was formed.
From a purely geometric point of view, such an artificially created combined structure of spacetime can be legitimate when the correct continuity of the metric of the individual regions is modeled. More complicated is the question of how such a structure can realistically arise during the gravitational collapse of a star..?.. There is no known mechanism that could cause a phase transition of the macroscopic space-time inside the collapsing star into a state of a new "false vacuum" with negative energy. Likewise, the formation of a thin layer of extremely dense matter in the region around the horizon. Thus, gravastars are probably not products of the gravitational collapse of massive stars.
   There was even an additional hypothesis that one gravastar could be nested inside another - a so-called nestar (perhaps a bit too sci-fi already?)...

We do not yet fully understand the final stages of gravitational collapse, especially in regions around singularities. Existing physical theories are reaching the limits of their validity here - the singularity is a certain indicator of the violation of Einstein's equations, probably under pressure of quantum laws. It can be expected that further theoretical research (especially in the field of quantum gravity and unitary field), together with careful astronomical observations, will shed new light on the problems of the final state during gravitational collapse.

4.8. Astrophysical significance of black holes		5.1. Basic principles of cosmology

Vojtech Ullmann