Towards Black Hole Entropy in Shape Dynamics

TL;DR

This paper demonstrates that black hole thermodynamics and entropy can be consistently defined within shape dynamics by treating the event horizon as an interior boundary, aligning with results from general relativity.

Contribution

It shows how to recover black hole thermodynamics in shape dynamics, despite different gauge symmetries, by using the horizon as a boundary to define gauge-invariant entropy.

Findings

Black hole entropy in shape dynamics matches that of general relativity.

Treating the horizon as a boundary allows for gauge-invariant thermodynamic definitions.

Shape dynamics can incorporate black hole thermodynamics consistently.

Abstract

Shape dynamics is classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Since the area of the event horizon of a black hole transforms under a generic spatial Weyl transformation, there has been some doubt that one can speak sensibly about the thermodynamics of black holes in shape dynamics. The purpose of this paper is to show that by treating the event horizon of a black hole as an interior boundary, one can recover familiar notions of black hole thermodynamics in shape dynamics and define a gauge invariant entropy that agrees with general relativity.