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
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
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 . 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.