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

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.

arXiv comment35 pages. v2: references added, minor modifications

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Cited by in corpus (7)

• The Large D Limit of Einstein's Equations
• An entropy current for dynamical black holes in four-derivative theories of gravity
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D
• Stress Tensor for Large-$D$ membrane at subleading orders
• An entropy current and the second law in higher derivative theories of gravity