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Journal Article

Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics


Eling,  Christopher
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Eling, C., Meyer, A., & Oz, Y. (2012). Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics. Journal of high energy physics: JHEP, 2012(08): 088. Retrieved from

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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.