Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics

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.

28 pages, 2 appendices; v2: added references, fixed typos, one clarifying comment

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• Drag force to all orders in gradients
• Petrov type I Spacetime and Dual Relativistic Fluids
• Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
• Noncomutativity in near horizon symmetries in gravity
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Constraints on Rindler Hydrodynamics
• Entropy Current and Fluid-Gravity Duality in Gauss-Bonnet theory
• Entropy-current for dynamical black holes in Chern-Simons theories of gravity
• Dynamical entropy of charged black objects
• Rindler Fluid with Weak Momentum Relaxation
• An entropy current and the second law in higher derivative theories of gravity