The Statistical Mechanics of Black Hole Thermodynamics

TL;DR

This paper explores the microscopic origins of black hole entropy, proposing a semi-classical and quantum gravity framework that suggests spacetime discreteness is essential for understanding horizon entropy.

Contribution

It offers a near-proof of the entropy increase law in semi-classical and quantum gravity contexts, emphasizing the role of spacetime discreteness in black hole thermodynamics.

Findings

Entropy increase law is supported in semi-classical approximation.

Spacetime discreteness may be necessary for finite horizon entropy.

Potential to count spacetime 'atoms' from horizon entropy.

Abstract

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''.