1997/05/31 by Rafael D. Sorkin
Physics and Astronomy · #gr-qc #hep-th
published as in Black Holes and Relativistic Stars, edited by R.M. Wald (University of Chicago Press, 1998) · 21 pages, plainTeX, no figures. (Only nontrivial change from original version is rewriting to improve clarity.)
arxiv created 1997/12/15 · arxiv updated 2009/11/30
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''.