Black Brane Entropy and Hydrodynamics

Abstract

A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics of higher dimensional black holes. This Letter introduces a correspondence between phenomenologically defined entropy currents in relativistic hydrodynamics and quasilocal horizons of near-equilibrium black objects in a dual gravitational description. A general formula is given, expressing the divergence of the entropy current in terms of geometric objects which appear naturally in the gravity dual geometry. The proposed definition is explicitly covariant with respect to boundary diffeomorphisms and reproduces known results when evaluated for the event horizon.

v2: much expanded, to appear in Phys. Rev D (Rapid Communications); v3: fixed arxiv.org metadata

References in corpus (17)

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• Fluid dynamics of R-charged black holes
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• Entropy Current in Conformal Hydrodynamics
• Universal hydrodynamics of non-conformal branes
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Cited by in corpus (18)

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• On the hydrodynamic attractor of Yang-Mills plasma
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• Spacetime near isolated and dynamical trapping horizons
• The large proper-time expansion of Yang-Mills plasma as a resurgent transseries
• AdS/Ricci-flat correspondence
• Black-hole horizons as probes of black-hole dynamics II: geometrical insights
• An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
• On the apparent horizon in fluid-gravity duality
• Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics
• Hydrodynamic attractors for the speed of sound in holographic Bjorken flow
• Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters
• Entropy currents from holography in hydrodynamics with charge
• Entropy production from quasinormal modes
• Relativistic Holographic Hydrodynamics from Black Hole Horizons
• Hybrid thermalization in the large $N$ limit
• On thermalization of a boost-invariant non Abelian plasma
• Quantum origin of the Minkowski space