Large D membrane for Higher Derivative Gravity and Black Hole Second Law

TL;DR

This paper derives effective membrane equations and an entropy current for black holes in Einstein-Gauss-Bonnet gravity at large dimensions, ensuring a local second law and analyzing stationary solutions.

Contribution

It provides the first derivation of membrane equations non-perturbative in the Gauss-Bonnet parameter at large D, extending the membrane paradigm to higher derivative gravity.

Findings

Derived effective membrane equations at large D for Einstein-Gauss-Bonnet gravity.

Constructed an entropy current satisfying a local second law.

Obtained explicit membrane stress tensor and stationary solutions.

Abstract

We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in $1/D$ upto linear order in the Gauss-Bonnet (GB) parameter $\beta$. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in $1/D$ but non-perturbatively in $\beta$ for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.