Holography, Gauge-Gravity Connection and Black Hole Entropy

TL;DR

This paper explores holography and gauge theories in black hole thermodynamics, deriving a criterion for stability and expressing entropy through a boundary gauge theory with quantum corrections.

Contribution

It introduces a novel approach to holography in black hole thermodynamics, deriving from elementary considerations and linking horizon degrees of freedom to a topological gauge theory.

Findings

Derived a holographic criterion for black hole stability.

Expressed black hole entropy in terms of horizon gauge theory.

Quantified quantum corrections to the area-law entropy.

Abstract

The issues of holography and possible links with gauge theories in spacetime physics is discussed, in an approach quite distinct from the more restricted AdS-CFT correspondence. A particular notion of holography in the context of black hole thermodynamics is derived (rather than conjectured) from rather elementary considerations, which also leads to a criterion of thermal stability of radiant black holes, without resorting to specific classical metrics. For black holes that obey this criterion, the canonical entropy is expressed in terms of the microcanonical entropy of an Isolated Horizon which is essentially a local generalization of the very global event horizon and is a null inner boundary of spacetime, with marginal outer trapping. It is argued why degrees of freedom on this horizon must be described by a topological gauge theory. Quantizing this boundary theory leads to the microcanonical entropy of the horizon expressed in terms of an infinite series asymptotic in the cross-sectional area, with the leading `area-law' term followed by finite, unambiguously calculable corrections arising from quantum spacetime fluctuations.