Membrane paradigm for Einstein-Gauss-Bonnet gravity

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.

v2: 18 pages, presentation improved, discussion section replaced, references updated, matches published version (excepting bibliographic details)

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• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Holographic Forced Fluid Dynamics in Non-relativistic Limit
• Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity
• Ringdown of Charged Compact Objects using Membrane Paradigm
• DC Conductivity and Higher Derivative Gravity
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• On the physical process first law for dynamical black holes
• Black Hole Entropy production and Transport coefficients in Lovelock Gravity
• Black hole mass formula in the membrane paradigm
• Hysteresis in $\eta /s$ for QFTs dual to spherical black holes
• Final state of instabilities in Born-Infeld black holes