Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

Details Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

2011-11-04

arxiv.org/abs/1111.1242v3

JHEP 1202 (2012) 006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification

Scientific paper

10.1007/JHEP02(2012)006

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.

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