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

Towards Black Hole Entropy in Shape Dynamics