Holography, CFT and Black Hole Entropy

TL;DR

This paper explores holographic principles in black hole thermodynamics, linking horizon degrees of freedom to conformal field theories, deriving entropy corrections, and establishing stability criteria for radiant black holes.

Contribution

It introduces a topological model for horizon degrees of freedom, connects them to 2D CFTs, and derives a universal stability bound for black holes.

Findings

Black hole entropy matches Bekenstein-Hawking with quantum corrections.

A universal stability bound relates black hole mass and entropy.

Phase transition behavior identified at stability boundary.

Abstract

Aspects of holography or dimensional reduction in gravitational physics are discussed with reference to black hole thermodynamics. Degrees of freedom living on Isolated Horizons (as a model for macroscopic, generic, eternal black hole horizons) are argued to be topological in nature and counted, using their relation to two dimensional conformal field theories. This leads to the microcanonical entropy of these black holes having the Bekenstein-Hawking form together with finite, unambigious {\it quantum spacetime} corrections. Another aspect of holography ensues for radiant black holes treated as a standard canonical ensemble with Isolated Horizons as the mean (equilibrium) configuration. This is shown to yield a universal criterion for thermal stability of generic radiant black holes, as a lower bound on the mass of the equilibrium isolated horizon in terms of its microcanonical entropy. Saturation of the bound occurs at a phase boundary separating thermally stable and unstable phases with symptoms of a first order phase transition.