Membrane paradigm and horizon thermodynamics in Lanczos-Lovelock gravity

A bstract 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 S Wald of the horizon when we consider a specific m -th order Lanczos-Lovelock model, through the relation , 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 .