

During the past 30 years, research in the theory of black holes
in general relativity has brought to light strong hints of a very
deep and fundamental relationship between gravitation,
thermodynamics, and quantum theory. The cornerstone of this
relationship is black hole thermodynamics, where it appears that
certain laws of black hole mechanics are, in fact, simply the
ordinary laws of thermodynamics applied to a system containing a
black hole. Indeed, the discovery of the thermodynamic behavior
of black holes - achieved primarily by classical and
semiclassical analyses - has given rise to most of our present
physical insights into the nature of quantum phenomena occurring
in strong gravitational fields.
The purpose of this article is to provide a review of the
following aspects of black hole thermodynamics:
- At the purely classical level, black holes in general
relativity (as well as in other diffeomorphism covariant
theories of gravity) obey certain laws which bear a remarkable
mathematical resemblance to the ordinary laws of
thermodynamics. The derivation of these laws of classical black
hole mechanics is reviewed in section
2
.
- Classically, black holes are perfect absorbers but do not
emit anything; their physical temperature is absolute zero.
However, in quantum theory black holes emit Hawking radiation
with a perfect thermal spectrum. This allows a consistent
interpretation of the laws of black hole mechanics as
physically corresponding to the ordinary laws of
thermodynamics. The status of the derivation of Hawking
radiation is reviewed in section
3
.
- The
generalized second law
(GSL) directly links the laws of black hole mechanics to the
ordinary laws of thermodynamics. The arguments in favor of the
GSL are reviewed in section
4
. A discussion of entropy bounds is also included in this
section.
- The classical laws of black hole mechanics together with
the formula for the temperature of Hawking radiation allow one
to identify a quantity associated with black holes - namely
A
/4 in general relativity - as playing the mathematical role of
entropy. The apparent validity of the GSL provides strong
evidence that this quantity truly is the physical entropy of a
black hole. A major goal of research in quantum gravity is to
provide an explanation for - and direct derivation of - the
formula for the entropy of a black hole. A brief survey of work
along these lines is provided in section
5
.
- Although much progress has been made in our understanding
of black hole thermodynamics, many important issues remain
unresolved. Primary among these are the ``black hole
information paradox'' and issues related to the degrees of
freedom responsible for the entropy of a black hole. These
unresolved issues are briefly discussed in section
6
.
Throughout this article, we shall set
, and we shall follow the sign and notational conventions of [99
]. Although I have attempted to make this review be reasonably
comprehensive and balanced, it should be understood that my
choices of topics and emphasis naturally reflect my own personal
viewpoints, expertise, and biases.


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The Thermodynamics of Black Holes
Robert M. Wald
http://www.livingreviews.org/lrr-2001-6
© Max-Planck-Gesellschaft. ISSN 1433-8351
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