AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy | Gravity, black holes and physics |
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 10^{8 }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/cm^{3},
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 ~10^{10}) 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 10^{20} 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..?..
So far, we are still far from understanding the final stages of gravitational collapse, especially in the areas 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.
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 |