Reparametrization Symmetry of Local Entropy Production on a Dynamical Horizon

Abstract

Recently, it has been shown that for a dynamical black hole in any higher derivative theory of gravity, one could construct a spatial entropy current, characterizing the in/outflow of entropy at every point on the horizon, as long as the dynamics of the amplitude is small enough. However, the construction is very much dependent on how we choose the spatial slicing of the horizon along its null generators. In this note, we have shown that though both the entropy density and the spatial entropy current change non-trivially under a reparametrization of the null generator, the net entropy production, which is given by the `time' derivative of entropy density plus the divergence of the spatial current is invariant. We have explicitly verified this claim for the particular case of dynamical black holes Einstein-Gauss-Bonnet theory.

arXiv commentPublished version

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Cited by in corpus (5)

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• The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
• Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields
• Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity
• Generalized Second Law for Non-minimally Coupled Matter Theories