Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics

TL;DR

This paper constructs a local entropy current in higher-curvature gravity theories within the fluid/gravity correspondence, demonstrating its non-negative divergence in dynamical Rindler horizons, thus extending the understanding of entropy in non-stationary spacetimes.

Contribution

It proposes a method to define an unambiguous local entropy current in higher-curvature gravity, resolving ambiguities present in non-stationary cases, and computes it explicitly for perturbed Rindler horizons.

Findings

The entropy current's divergence is non-negative at second order in fluid gradients.

Ambiguities in defining the entropy current can be eliminated by a gauge choice.

Explicit second-order calculations confirm the physical consistency of the proposed entropy current.

Abstract

In the hydrodynamic regime of field theories the entropy is upgraded to a local entropy current. The entropy current is constructed phenomenologically order by order in the derivative expansion by requiring that its divergence is non-negative. In the framework of the fluid/gravity correspondence, the entropy current of the fluid is mapped to a vector density associated with the event horizon of the dual geometry. In this work we consider the local horizon entropy current for higher-curvature gravitational theories proposed in arXiv:1202.2469, whose flux for stationary solutions is the Wald entropy. In non-stationary cases this definition contains ambiguities, associated with absence of a preferred timelike Killing vector. We argue that these ambiguities can be eliminated in general by choosing the vector that generates the subset of diffeomorphisms preserving a natural gauge condition on the bulk metric. We study a dynamical, perturbed Rindler horizon in Einstein-Gauss-Bonnet gravity setting and compute the bulk dual solution to second order in fluid gradients. We show that the corresponding unambiguous entropy current at second order has a manifestly non-negative divergence.