The case for black hole thermodynamics, Part II: statistical mechanics

TL;DR

This paper argues that black hole thermodynamics can be explained through statistical mechanics, supported by calculations in quantum gravity, string theory, and the AdS/CFT correspondence, making a strong case for black holes as thermodynamic systems.

Contribution

It provides a detailed review and synthesis of evidence from quantum gravity, string theory, and AdS/CFT to support black hole thermodynamics as a statistical-mechanical phenomenon.

Findings

Quantum field theory calculations support black hole entropy.

String theory results align with thermodynamic predictions.

AdS/CFT correspondence reproduces black hole statistical mechanics structure.

Abstract

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. (Here I presume that black holes are indeed thermodynamic systems in the fullest sense; I review the evidence for \emph{that} conclusion in the prequel to this paper.) I focus on three lines of argument: (i) zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; (ii) calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (iii) recovery of the qualitative and (in some cases) quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used (effective field theory; string theory; AdS/CFT) at a (relatively) introductory level: the paper is aimed at students and non-specialists and does not presume advanced knowledge of quantum gravity.. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity.