Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-05-05
in Black Holes and Relativistic Stars, edited by R.M. Wald (University of Chicago Press, 1998)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages, plainTeX, no figures. (Only nontrivial change from original version is rewriting to improve clarity.)
Scientific paper
Although we have convincing evidence that a black hole bears an entropy proportional to its surface (horizon) area, the ``statistical mechanical'' explanation of this entropy remains unknown. Two basic questions in this connection are: what is the microscopic origin of the entropy, and why does the law of entropy increase continue to hold when the horizon entropy is included? After a review of some of the difficulties in answering these questions, I propose an explanation of the law of entropy increase which comes near to a proof in the context of the ``semi-classical'' approximation, and which also provides a proof in full quantum gravity under the assumption that the latter fulfills certain natural expectations, like the existence of a conserved energy definable at infinity. This explanation seems to require a fundamental spacetime discreteness in order for the entropy to be consistently finite, and I recall briefly some of the ideas for what the discreteness might be. If such ideas are right, then our knowledge of the horizon entropy will allow us to ``count the atoms of spacetime''.
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