A membrane paradigm at large D

Abstract

We study $SO(d+1)$ invariant solutions of the classical vacuum Einstein equations in $p+d+3$ dimensions. In the limit $d\to \infty$ with $p$ held fixed we construct a class of solutions labelled by the shape of a membrane (the event horizon), together with a `velocity' field that lives on this membrane. We demonstrate that our metrics can be corrected to nonsingular solutions at first sub-leading order in $\frac{1}{d}$ if and only if the membrane shape and `velocity' field obey equations of motion which we determine. These equations define a well posed initial value problem for the membrane shape and this `velocity' and so completely determinethe dynamics of the black hole. They may be viewed as governing the non-linear dynamics of the light quasi normal modes of Emparan, Suzuki and Tanabe.

The main results emphasised better, The presentation of the quasinormal modes improved for clarity and typos corrected

References in corpus (5)

• Nonlinear Fluid Dynamics from Gravity
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Local Fluid Dynamical Entropy from Gravity
• Effective theory of Black Holes in the 1/D expansion
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion

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