Reparametrization Symmetry of Local Entropy Production on a Dynamical Horizon

TL;DR

This paper demonstrates that the net entropy production on a dynamical black hole horizon remains invariant under reparametrizations of null generators, despite changes in entropy density and current, verified explicitly in Einstein-Gauss-Bonnet gravity.

Contribution

It establishes the reparametrization invariance of net entropy production for dynamical horizons in higher derivative gravity theories.

Findings

Net entropy production is invariant under null generator reparametrizations.

Explicit verification in Einstein-Gauss-Bonnet gravity confirms the invariance.

The construction of entropy current depends on horizon slicing, but net entropy production does not.

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.