Introduction: Brief History of Black Hole Physics
A black hole is, by definition, a region in spacetime in which the gravitational field is
so strong that it precludes even light from escaping to infinity.
A black hole is formed when a body of mass M contracts to a size less than the so-
called gravitational radius rg = 2GM/c2 (G is Newton's gravitational constant, and
с is the speed of light). The velocity required to leave the boundary of the black hole
and move away to infinity (the escape velocity) equals the speed of light. One easily
concludes then that neither signals nor particles can escape from the region inside
the black hole since the speed of light is the limiting propagation velocity for physical
signals. This conclusion is of absolute nature in Einstein's theory of gravitation
because the gravitational interaction is universal. The role of gravitational charge is
played by mass whose value is proportional to the total energy of the system. Hence,
all objects with nonzero energy participate in the gravitational interaction.
Einstein's theory of gravitation, alias general relativity, is employed to the full in
the description of black holes. It may appear at first glance that one cannot hope
to obtain an acceptably complete description of black holes, owing to the complex-
ity of the equations involved and, among other factors, their essential nonlinearity.
Fortunately, it was found that shortly after its formation, any black hole becomes
stationary, and its field is determined in a unique manner by a small number of pa-
rameters; namely, its mass and angular momentum, and its electric charge (if it is
charged). The physical reason for this striking property of black holes is the fact that
in the extremely strong field of a black hole in empty space, only very special types of
configuration of physical fields (including the gravitational field) can be stationary.
Since signals cannot escape from a black hole, while physical objects and radiation
can fall into it, the surface bounding the black hole in spacetime (called the event
horizon) is a lightlike surface. The birth of a black hole signifies the formation of a
non-trivial causal structure in spacetime. As a result of these specific features, new
methods had to be developed to analyze the interaction of black holes with physical
fields and matter, and with other black holes.
The term "black hole" was introduced by Wheeler in 1967 although the theoretical
study of these object has quite a long history. The very possibility of the existence of
such objects was first discussed by Michell and Laplace within the framework of the
Newtonian theory at the end of the 18th century [see Barrow and Silk (983), Israel
(987), Novikov (990)]. In fact, in general relativity, the problem arose within a year
after the theory had been developed, i.e., after Schwarzschild A916) obtained the first
exact (spherically symmetric) solution of Einstein's equations in vacuum. In addition
to a singularity at the center of symmetry (at r = 0), this solution had an additional
singularity on the gravitational-radius surface (at r = rg). More than a third of a
century elapsed before a profound understanding of the structure of spacetime in
strong gravitational fields was achieved as a result of analyses of the "unexpected"
features of the Schwarzschild solution by Flamm (1916), Weyl (1917), Eddington
(1924), Lemaitre (1933), Einstein and Rosen (1935), and the complete solution of
the formulated problem was obtained [Synge (1950), Finkelstein (1958), Fronsdal
(1959), Kruskal (1960), Szekeres (1960), Novikov (1963, 1964a)]. The length of this
interval may have been influenced by the general belief that nature could not admit
a body whose size would be comparable to its gravitational radius; this viewpoint
was shared by the creator of general relativity himself [see e.g., Israel A987) and
references therein]. Some interest in the properties of very compact gravitational
systems was stimulated in the thirties after Chandrasekhar's A931) work on white
dwarfs and the works of Landau (1932), Baade and Zwicky (1934), and Oppenheimer
and Volkoff (1939) who showed that neutron stars are possible, with a radius only
a few times that of the gravitational radius. The gravitational collapse of a massive
star which produces a black hole was first described by Oppenheimer and Snyder
(1939).
The next period began in the middle sixties when intensive theoretical studies
were initiated on the general properties of black holes and their classical interactions,
after the work of Synge (1950), Kruskal (1960) and others who obtained the com-
plete solution for the Schwarzschild problem, and of Kerr (1963) who discovered a
solution describing the gravitational field of a rotating black hole. Before this pe-
riod specialists had considered black holes as dead objects, ultimate final stage of
the evolution of massive stars, and probably of more massive objects. The names
"frozen" or "collapsed" stars used by specialists until the end of sixties for the de-
scription of these objects reflected such an attitude. This point of view proved to
be rather restrictive when processes in the close vicinity of these objects became the
focus of interest. Moreover, it prevents from the outset even formulating any ideas
concerning the physical processes inside them. In the middle of the sixties a new
approach (paradigm) gained ascendancy in the community of theorists working in
general relativity (but not among astronomers who mainly were very far from the
problems of black holes, and even discussions of these problems were not welcomed
in the "decent society"!). This new point of view was a historical development of the
route initiated by the work of Oppenheimer and Snyder (1939), where it was shown
that an observer on the surface of a collapsing star sees no "freezing" at all, but can
register events both outside and inside the gravitational radius. This point of view
implied that an object formed after the gravitational collapse could be considered in
some sense as a "hole" in spacetime.
Just at this time Wheeler (1968) coined the name "black hole". When in 1992 we
started working on this book in Copenhagen, John Wheeler visited us and in very
lively fashion recalled his lecture in late 1967 when he used this name for the first
time (see Figure 1.1). Soon after that this name was adopted enthusiastically by
everybody. We believe that readers would agree that this graphic expression reflects
very picturesquely the remarkable properties of the object.
The now-classic theorems stating that "black holes have no hair" (that is, no
external individual attributes except mass, angular momentum, and charge), that
a black hole contains a singularity inside it, and that the black hole area cannot
decrease were proved during this period. These and other results made it possible to
construct a qualitative picture of the formation of a black hole, its possible further
evolution, and its interaction with matter and classical physical fields. Many of these
results were summarized in the well-known monographs of Zel'dovich and Novikov
(1967b, 1971a,b), Misner, Thorne, and Wheeler (1973), Hawking and Ellis (1973),
Thorne, Price, and Macdonald (1986), and Novikov and Frolov (1989).
After pulsars (neutron stars) were discovered at the end of the sixties, astrophysi-
cists had to examine the prospects for the observational detection of black holes. The
analysis of the accretion of matter onto isolated black holes and onto black holes in
binary systems predicted that accreting black holes may constitute powerful sources
of X-rays [Novikov and Zel'dovich (1966), Shklovsky (1967b), Burbidge (1972)]. The
progress of X-ray astronomy and the studies using X-ray satellites that began in
the 1970's led to the discovery of a number of X-ray sources. The hypothesis was
proposed that some of them are black holes in binary stellar systems.
More than 25 years of constant study of these objects provided confirmation of
the initial hypothesis. Now at the end of nineties we are sure that black holes with
stellar masses do exist in a number of binaries in our Galaxy [Thorne (1994b)]. There
is also good reason to believe that the nuclei of active galaxies (and possibly of any
galaxy) and quasars contain massive or supermassive black holes [see Blandford and
Thorne (1979), Rees (1982), Begelman and Rees (1996)]. Two recent discoveries -
one by astronomers using the Hubble Telescope [Ford et al. (1994), Harms et al.
(1994)], the other by radioastronomers [Miyoshi et al. (1995)] - gave clear evidence
for huge black holes in the centers of galaxies. In both cases observations revealed
disks of gas orbiting the central objects, and it is possible to give robust arguments
that these objects can be nothing but supermassive black holes.
The discussion of the possible observational aspects of black hole study drew
considerable attention to the problem of the motion of particles and propagation of
physical fields in the spacetime of stationary black holes. This problem, which is pre-
Brief History of Black Hole Physics
dominantly mathematical and involves the integration of the equations of geodesies
and the solution (by expansion in eigenfunctions) of the wave equations in the Kerr
metric, has now been completely solved. Numerous relevant results are summarized
in the monograph by Chandrasekhar (1983).
The sensational "news" of the possible discovery of a black hole in an X-ray
binary (Cygnus X-i) had scarcely died down when a new unexpected result obtained
by Hawking (1974, 1975) again focussed physicists' attention on black holes. It was
found that as a result of the instability of the vacuum in the strong gravitational
field of a black hole, these objects are sources of quantum radiation. The most
intriguing property of this radiation is that it has a thermal spectrum. In other
words, if one neglects the scattering of the radiation by the external gravitational
field, a black hole radiates like a heated black body. If the black hole mass is small,
it decays over a time shorter than the age of the Universe. Such small black holes,
now called primordial black holes, may have been formed only at a very early stage
of the Universe's evolution [Zel'dovich and Novikov (1966, 1967b), Hawking (1971)].
In principle, the discovery of primordial black holes or of their decay products would
supply valuable information on the physical processes occurring in the Universe at
that period.
Hawking's discovery stimulated a large number of papers which analyzed specific
features of quantum effects in black holes. In addition to a detailed description of the
effects due to the creation of real particles escaping to infinity, substantial progress
has been achieved in the understanding of the effect of vacuum polarization in the
vicinity of a black hole. This effect is important for the construction of a complete
quantum description of an "evaporating" black hole.1
It is quite interesting that not so many (say 15-20) years ago, black holes were
considered as highly exotic objects, and the general attitude in the wider physical
and astrophysical community (i.e., among the scientists who were not working on
this subject) to these objects was quite cautious. Now the situation has changed
drastically. It happened both because of new astrophysical data and because of the
development of the theory.
In binary systems and in galactic centers, accretion of gas onto a black hole
generates radiation of light or X-rays. The efficiency of this process is so high that
the accretion of matter onto a black hole is one of the most powerful energy sources
in the Universe. That is why black holes recently became the favored hypothesis for
trying to explain processes with huge energy release from compact regions of space.
This is what gives black holes their current importance in astrophysics.
'There were a number of review articles written in the 1970's and early 1980's which had summa-
rized main results obtained during this "heroic" period of black hole physics. These are references
to some of them: Penrose A972), Carter (1973a, 1976), Sexl A975), Israel (1983), Markov (1970,
1973), De Witt (1975), Sciama (1976), Dymnikova (1986), Bekenstein (1980), Ruffini (1979), Frolov
(1976b, 1978b, 1983b). See also a remarkable review article by Israel (1987) which describes the
history of evolution of the black hole idea.
More recently another aspect of black hole physics became very important for
astrophysical applications. The collision of a black hole with a neutron star or coa-
lescence of a pair of black holes in binary systems is a powerful source of gravitational
radiation which might be strong enough to reach the Earth and be observed in a new
generation of gravitational wave experiments (LIGO, LISA, and others). The de-
tection of gravitational waves from these sources requires a detailed description of
the gravitational field of a black hole during the collision. In principle, gravitational
astronomy opens remarkable opportunities to test gravitational field theory in the
limit of very strong gravitational fields. In order to be able to do this, besides the
construction of the gravitational antennas, it is also necessary to obtain the solution
of the gravitational equations describing this type of situation. Until now there exist
no analytical tools which allow this to be done. Under these conditions one of the
important problems is the numerical study of colliding black holes.
Besides its direct astrophysical application, the physics of black holes has a more
general importance. The existence of black holes introduces into physics a new con-
cept which can be called the concept of invisibility. In the presence of a black hole,
physically important classes of observers, at rest or moving in the black hole exterior
(external observers), would agree that there exists a spacetime region which is in
principle unobservable in their reference frame. Since exactly these frames are used
in astrophysics, we have a situation which never occurred before. Is there any sense
in discussing what happens inside a black hole if there is no way to compare our
predictions with observations outside a black hole or to transfer our knowledge to the
external observer if we decide to dive into a black hole? Perhaps the general answer
to this almost philosophical question lies somewhere outside physics itself.2
The very existence of "invisible" regions ("holes") in spacetime has a number of
important physical consequences. One of them is the thermal nature of the Hawking
radiation. In the process of black hole formation the information concerning the
state of quantum fields inside the horizon is lost for an external observer. Even if at
the beginning (before the collapse) a system was in a pure quantum state, after the
black hole formation the state outside the horizon is mixed, and it is described by
a density matrix. According to Hawking, this density matrix is thermal. In other
words, the combination of gravity and quantum mechanics in the presence of black
holes requires for its consistency the introduction of thermodynamical methods. The
statistical mechanical foundations of the thermodynamics of black holes still remain
one of the most intriguing problems in theoretical physics.
An important new development of black hole physics is connected with the at-
tempts to construct a unified theory of all interactions. Unification of gravity with
other gauge theories made it interesting to study black-hole-like solutions, describ-
ing a black hole with "colored" and "quantum hair". Modern superstring theory,
2We should add here that the standard assertion about the impossibility of seeing what, happens
inside a black hole is to be taken with care. A gedanken experiment, has been proposed [Frolov and
Novikov (1993a)] where one can probe a black hole interior.
which explains gravity as some collective state of fundamental string excitations, re-
produces general relativity in the low energy limit. This theory requires additional
fundamental fields (e.g., the dilaton field), which inevitably violate the equivalence
principle. The study of Ыаск-hole-like solutions in string-generated gravity attracted
the attention of theorists, many of whom have been working in high energy physics
and superstring theory.
Besides the main solved and unsolved problems in black hole physics listed above,
there are a lot of other questions connected with black hole physics and its applica-
tions. It is now virtually impossible to write a book where all these problems and
questions are discussed in detail. Every month new issues of Physical Review D,
Astrophysical Journal, and other physical and astrophysical journals add scores of
new publications on the subject of black holes. In writing a book on this subject we
were restricted by space and time. We tried to include material that is connected to
the basic concepts of black hole physics and their recent development. Both of the
authors have been working in the area of black hole physics for more than 30 years.
Certainly we have our favorite topics. The reader should excuse the authors if some
subjects are treated in more detail than other that are more important from his oi-
lier point of view.
|
so strong that it precludes even light from escaping to infinity.
A black hole is formed when a body of mass M contracts to a size less than the so-
called gravitational radius rg = 2GM/c2 (G is Newton's gravitational constant, and
с is the speed of light). The velocity required to leave the boundary of the black hole
and move away to infinity (the escape velocity) equals the speed of light. One easily
concludes then that neither signals nor particles can escape from the region inside
the black hole since the speed of light is the limiting propagation velocity for physical
signals. This conclusion is of absolute nature in Einstein's theory of gravitation
because the gravitational interaction is universal. The role of gravitational charge is
played by mass whose value is proportional to the total energy of the system. Hence,
all objects with nonzero energy participate in the gravitational interaction.
Einstein's theory of gravitation, alias general relativity, is employed to the full in
the description of black holes. It may appear at first glance that one cannot hope
to obtain an acceptably complete description of black holes, owing to the complex-
ity of the equations involved and, among other factors, their essential nonlinearity.
Fortunately, it was found that shortly after its formation, any black hole becomes
stationary, and its field is determined in a unique manner by a small number of pa-
rameters; namely, its mass and angular momentum, and its electric charge (if it is
charged). The physical reason for this striking property of black holes is the fact that
in the extremely strong field of a black hole in empty space, only very special types of
configuration of physical fields (including the gravitational field) can be stationary.
Since signals cannot escape from a black hole, while physical objects and radiation
can fall into it, the surface bounding the black hole in spacetime (called the event
horizon) is a lightlike surface. The birth of a black hole signifies the formation of a
non-trivial causal structure in spacetime. As a result of these specific features, new
methods had to be developed to analyze the interaction of black holes with physical
fields and matter, and with other black holes.
The term "black hole" was introduced by Wheeler in 1967 although the theoretical
study of these object has quite a long history. The very possibility of the existence of
such objects was first discussed by Michell and Laplace within the framework of the
Newtonian theory at the end of the 18th century [see Barrow and Silk (983), Israel
(987), Novikov (990)]. In fact, in general relativity, the problem arose within a year
after the theory had been developed, i.e., after Schwarzschild A916) obtained the first
exact (spherically symmetric) solution of Einstein's equations in vacuum. In addition
to a singularity at the center of symmetry (at r = 0), this solution had an additional
singularity on the gravitational-radius surface (at r = rg). More than a third of a
century elapsed before a profound understanding of the structure of spacetime in
strong gravitational fields was achieved as a result of analyses of the "unexpected"
features of the Schwarzschild solution by Flamm (1916), Weyl (1917), Eddington
(1924), Lemaitre (1933), Einstein and Rosen (1935), and the complete solution of
the formulated problem was obtained [Synge (1950), Finkelstein (1958), Fronsdal
(1959), Kruskal (1960), Szekeres (1960), Novikov (1963, 1964a)]. The length of this
interval may have been influenced by the general belief that nature could not admit
a body whose size would be comparable to its gravitational radius; this viewpoint
was shared by the creator of general relativity himself [see e.g., Israel A987) and
references therein]. Some interest in the properties of very compact gravitational
systems was stimulated in the thirties after Chandrasekhar's A931) work on white
dwarfs and the works of Landau (1932), Baade and Zwicky (1934), and Oppenheimer
and Volkoff (1939) who showed that neutron stars are possible, with a radius only
a few times that of the gravitational radius. The gravitational collapse of a massive
star which produces a black hole was first described by Oppenheimer and Snyder
(1939).
The next period began in the middle sixties when intensive theoretical studies
were initiated on the general properties of black holes and their classical interactions,
after the work of Synge (1950), Kruskal (1960) and others who obtained the com-
plete solution for the Schwarzschild problem, and of Kerr (1963) who discovered a
solution describing the gravitational field of a rotating black hole. Before this pe-
riod specialists had considered black holes as dead objects, ultimate final stage of
the evolution of massive stars, and probably of more massive objects. The names
"frozen" or "collapsed" stars used by specialists until the end of sixties for the de-
scription of these objects reflected such an attitude. This point of view proved to
be rather restrictive when processes in the close vicinity of these objects became the
focus of interest. Moreover, it prevents from the outset even formulating any ideas
concerning the physical processes inside them. In the middle of the sixties a new
approach (paradigm) gained ascendancy in the community of theorists working in
general relativity (but not among astronomers who mainly were very far from the
problems of black holes, and even discussions of these problems were not welcomed
in the "decent society"!). This new point of view was a historical development of the
route initiated by the work of Oppenheimer and Snyder (1939), where it was shown
that an observer on the surface of a collapsing star sees no "freezing" at all, but can
register events both outside and inside the gravitational radius. This point of view
implied that an object formed after the gravitational collapse could be considered in
some sense as a "hole" in spacetime.
Just at this time Wheeler (1968) coined the name "black hole". When in 1992 we
started working on this book in Copenhagen, John Wheeler visited us and in very
lively fashion recalled his lecture in late 1967 when he used this name for the first
time (see Figure 1.1). Soon after that this name was adopted enthusiastically by
everybody. We believe that readers would agree that this graphic expression reflects
very picturesquely the remarkable properties of the object.
The now-classic theorems stating that "black holes have no hair" (that is, no
external individual attributes except mass, angular momentum, and charge), that
a black hole contains a singularity inside it, and that the black hole area cannot
decrease were proved during this period. These and other results made it possible to
construct a qualitative picture of the formation of a black hole, its possible further
evolution, and its interaction with matter and classical physical fields. Many of these
results were summarized in the well-known monographs of Zel'dovich and Novikov
(1967b, 1971a,b), Misner, Thorne, and Wheeler (1973), Hawking and Ellis (1973),
Thorne, Price, and Macdonald (1986), and Novikov and Frolov (1989).
After pulsars (neutron stars) were discovered at the end of the sixties, astrophysi-
cists had to examine the prospects for the observational detection of black holes. The
analysis of the accretion of matter onto isolated black holes and onto black holes in
binary systems predicted that accreting black holes may constitute powerful sources
of X-rays [Novikov and Zel'dovich (1966), Shklovsky (1967b), Burbidge (1972)]. The
progress of X-ray astronomy and the studies using X-ray satellites that began in
the 1970's led to the discovery of a number of X-ray sources. The hypothesis was
proposed that some of them are black holes in binary stellar systems.
More than 25 years of constant study of these objects provided confirmation of
the initial hypothesis. Now at the end of nineties we are sure that black holes with
stellar masses do exist in a number of binaries in our Galaxy [Thorne (1994b)]. There
is also good reason to believe that the nuclei of active galaxies (and possibly of any
galaxy) and quasars contain massive or supermassive black holes [see Blandford and
Thorne (1979), Rees (1982), Begelman and Rees (1996)]. Two recent discoveries -
one by astronomers using the Hubble Telescope [Ford et al. (1994), Harms et al.
(1994)], the other by radioastronomers [Miyoshi et al. (1995)] - gave clear evidence
for huge black holes in the centers of galaxies. In both cases observations revealed
disks of gas orbiting the central objects, and it is possible to give robust arguments
that these objects can be nothing but supermassive black holes.
The discussion of the possible observational aspects of black hole study drew
considerable attention to the problem of the motion of particles and propagation of
physical fields in the spacetime of stationary black holes. This problem, which is pre-
Brief History of Black Hole Physics
dominantly mathematical and involves the integration of the equations of geodesies
and the solution (by expansion in eigenfunctions) of the wave equations in the Kerr
metric, has now been completely solved. Numerous relevant results are summarized
in the monograph by Chandrasekhar (1983).
The sensational "news" of the possible discovery of a black hole in an X-ray
binary (Cygnus X-i) had scarcely died down when a new unexpected result obtained
by Hawking (1974, 1975) again focussed physicists' attention on black holes. It was
found that as a result of the instability of the vacuum in the strong gravitational
field of a black hole, these objects are sources of quantum radiation. The most
intriguing property of this radiation is that it has a thermal spectrum. In other
words, if one neglects the scattering of the radiation by the external gravitational
field, a black hole radiates like a heated black body. If the black hole mass is small,
it decays over a time shorter than the age of the Universe. Such small black holes,
now called primordial black holes, may have been formed only at a very early stage
of the Universe's evolution [Zel'dovich and Novikov (1966, 1967b), Hawking (1971)].
In principle, the discovery of primordial black holes or of their decay products would
supply valuable information on the physical processes occurring in the Universe at
that period.
Hawking's discovery stimulated a large number of papers which analyzed specific
features of quantum effects in black holes. In addition to a detailed description of the
effects due to the creation of real particles escaping to infinity, substantial progress
has been achieved in the understanding of the effect of vacuum polarization in the
vicinity of a black hole. This effect is important for the construction of a complete
quantum description of an "evaporating" black hole.1
It is quite interesting that not so many (say 15-20) years ago, black holes were
considered as highly exotic objects, and the general attitude in the wider physical
and astrophysical community (i.e., among the scientists who were not working on
this subject) to these objects was quite cautious. Now the situation has changed
drastically. It happened both because of new astrophysical data and because of the
development of the theory.
In binary systems and in galactic centers, accretion of gas onto a black hole
generates radiation of light or X-rays. The efficiency of this process is so high that
the accretion of matter onto a black hole is one of the most powerful energy sources
in the Universe. That is why black holes recently became the favored hypothesis for
trying to explain processes with huge energy release from compact regions of space.
This is what gives black holes their current importance in astrophysics.
'There were a number of review articles written in the 1970's and early 1980's which had summa-
rized main results obtained during this "heroic" period of black hole physics. These are references
to some of them: Penrose A972), Carter (1973a, 1976), Sexl A975), Israel (1983), Markov (1970,
1973), De Witt (1975), Sciama (1976), Dymnikova (1986), Bekenstein (1980), Ruffini (1979), Frolov
(1976b, 1978b, 1983b). See also a remarkable review article by Israel (1987) which describes the
history of evolution of the black hole idea.
More recently another aspect of black hole physics became very important for
astrophysical applications. The collision of a black hole with a neutron star or coa-
lescence of a pair of black holes in binary systems is a powerful source of gravitational
radiation which might be strong enough to reach the Earth and be observed in a new
generation of gravitational wave experiments (LIGO, LISA, and others). The de-
tection of gravitational waves from these sources requires a detailed description of
the gravitational field of a black hole during the collision. In principle, gravitational
astronomy opens remarkable opportunities to test gravitational field theory in the
limit of very strong gravitational fields. In order to be able to do this, besides the
construction of the gravitational antennas, it is also necessary to obtain the solution
of the gravitational equations describing this type of situation. Until now there exist
no analytical tools which allow this to be done. Under these conditions one of the
important problems is the numerical study of colliding black holes.
Besides its direct astrophysical application, the physics of black holes has a more
general importance. The existence of black holes introduces into physics a new con-
cept which can be called the concept of invisibility. In the presence of a black hole,
physically important classes of observers, at rest or moving in the black hole exterior
(external observers), would agree that there exists a spacetime region which is in
principle unobservable in their reference frame. Since exactly these frames are used
in astrophysics, we have a situation which never occurred before. Is there any sense
in discussing what happens inside a black hole if there is no way to compare our
predictions with observations outside a black hole or to transfer our knowledge to the
external observer if we decide to dive into a black hole? Perhaps the general answer
to this almost philosophical question lies somewhere outside physics itself.2
The very existence of "invisible" regions ("holes") in spacetime has a number of
important physical consequences. One of them is the thermal nature of the Hawking
radiation. In the process of black hole formation the information concerning the
state of quantum fields inside the horizon is lost for an external observer. Even if at
the beginning (before the collapse) a system was in a pure quantum state, after the
black hole formation the state outside the horizon is mixed, and it is described by
a density matrix. According to Hawking, this density matrix is thermal. In other
words, the combination of gravity and quantum mechanics in the presence of black
holes requires for its consistency the introduction of thermodynamical methods. The
statistical mechanical foundations of the thermodynamics of black holes still remain
one of the most intriguing problems in theoretical physics.
An important new development of black hole physics is connected with the at-
tempts to construct a unified theory of all interactions. Unification of gravity with
other gauge theories made it interesting to study black-hole-like solutions, describ-
ing a black hole with "colored" and "quantum hair". Modern superstring theory,
2We should add here that the standard assertion about the impossibility of seeing what, happens
inside a black hole is to be taken with care. A gedanken experiment, has been proposed [Frolov and
Novikov (1993a)] where one can probe a black hole interior.
which explains gravity as some collective state of fundamental string excitations, re-
produces general relativity in the low energy limit. This theory requires additional
fundamental fields (e.g., the dilaton field), which inevitably violate the equivalence
principle. The study of Ыаск-hole-like solutions in string-generated gravity attracted
the attention of theorists, many of whom have been working in high energy physics
and superstring theory.
Besides the main solved and unsolved problems in black hole physics listed above,
there are a lot of other questions connected with black hole physics and its applica-
tions. It is now virtually impossible to write a book where all these problems and
questions are discussed in detail. Every month new issues of Physical Review D,
Astrophysical Journal, and other physical and astrophysical journals add scores of
new publications on the subject of black holes. In writing a book on this subject we
were restricted by space and time. We tried to include material that is connected to
the basic concepts of black hole physics and their recent development. Both of the
authors have been working in the area of black hole physics for more than 30 years.
Certainly we have our favorite topics. The reader should excuse the authors if some
subjects are treated in more detail than other that are more important from his oi-
lier point of view.
|
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