A Charged Membrane Paradigm at Large D

TL;DR

This paper develops a membrane paradigm for black hole horizons in Einstein-Maxwell theory at large spacetime dimensions, describing horizon dynamics as a well-posed initial value problem for a charged membrane in flat space.

Contribution

It introduces a geometric membrane framework for black hole horizon dynamics in large D Einstein-Maxwell theory, extending previous approaches to include charge and general symmetries.

Findings

Derived leading order membrane equations governing shape, charge density, and velocity.

Recast membrane equations into a symmetry-independent geometric form.

Established a well-posed initial value problem for horizon evolution.

Abstract

We study the effective dynamics of black hole horizons in Einstein-Maxwell theory in a large number of spacetime dimensions $D$. We demonstrate that horizon dynamics may be recast as a well posed initial value problem for the motion of a codimension one non gravitational membrane moving in flat space. The dynamical degrees of freedom of this membrane are its shape, charge density and a divergence free velocity field. We determine the equations that govern membrane dynamics at leading order in the large $D$ expansion. Our derivation of the membrane equations assumes that the solution preserves an SO$(D-p-2)$ isometry with $p$ held fixed as $D$ is taken to infinity. However we are able to cast our final membrane equations into a completely geometric form that makes no reference to this symmetry algebra.