Membrane paradigm and horizon thermodynamics in Lanczos-Lovelock gravity

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 η and ζ of the membrane fluid. We show that the membrane pressure is intimately connected with Noether charge entropy SWald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {p^{{\left( {\text{m}} \right)}}}A/T = \left[ {\left( {D - {2}m} \right)/\left( {D - {2}} \right)} \right]S_{\text{Wald}}^{{\left( {\text{m}} \right)}} $\end{document}, 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 ζ = −2(D − 3)/(D − 2)η.