Statistical Thermodynamics of a Black Hole in Terms of Surface Fields

TL;DR

This paper develops a statistical thermodynamics framework for black holes using surface fields at the horizon, deriving the Bekenstein-Hawking entropy from surface mode confinement and topology considerations.

Contribution

It introduces an action principle incorporating surface degrees of freedom at the black hole horizon, linking surface modes to entropy calculation.

Findings

Derivation of Bekenstein-Hawking entropy from surface mode confinement.

Identification of surface degrees of freedom as diffeomorphisms and opening angles.

Proposal of a novel statistical ensemble with an exponential-shaped volume constraint.

Abstract

An action principle for spacetimes with the topology of an Euclidean black-hole is given. The gravitational field is described by the ordinary volume degrees of freedom plus additional surface fields at the horizon. The surface degrees of freedom correspond to diffeomorphisms on the sphere at the horizon and a field of ``opening angles''. General covariance forces the surface modes to be confined to a box of an unusual exponential shape, whose volume must be specified as part of the definition of the statistical ensemble. This gives rise to the Bekenstein-Hawking entropy.