Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

TL;DR

This paper explores the membrane paradigm in Lanczos-Lovelock gravity, deriving expressions for membrane fluid properties and linking them to horizon entropy and energy in arbitrary dimensions.

Contribution

It provides compact formulas for membrane pressure and viscosity coefficients in Lanczos-Lovelock models, connecting them to horizon entropy and energy.

Findings

Membrane pressure relates to Wald entropy via a specific formula.

Viscosity coefficients are expressed in terms of horizon entropy and energy.

Bulk and shear viscosities obey a specific proportional relation.

Abstract

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.