Membrane paradigm for Einstein-Gauss-Bonnet gravity

TL;DR

This paper develops a membrane paradigm for black holes in Einstein-Gauss-Bonnet gravity, modeling the horizon as a fluid with specific transport properties, and computes relevant viscosity ratios.

Contribution

It extends the membrane paradigm to Einstein-Gauss-Bonnet gravity, deriving the stress tensor and transport coefficients for black hole horizons in higher dimensions.

Findings

The stress tensor can be regularized and expressed as a Newtonian viscous fluid.

Transport coefficients are computed for black holes with constant curvature horizons.

The shear viscosity to entropy density ratio matches previous results for black branes.

Abstract

We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions $ \ge 5$. As in the case of general relativity, the horizon can be modeled as a membrane endowed with fluidlike properties. We derive the stress tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross section, for which the stress tensor can be regularized with the usual redshift factor, and expressed in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. We evaluate the transport coefficients for black holes with constant curvature horizons and negative or zero cosmological constant. For the black brane geometry our result for the ratio of shear viscosity to entropy density agrees with that obtained previously in different frameworks.