Black Holes in Large Number of Dimensions

Abstract

We study the effective horizon dynamics of black holes in large number of dimensions($D$). To do this,we construct $SO(D-p-2)$ invariant solutions to Einstein's equations in large number of dimensions D in a power series expansion in $\frac{1}{D-3}$ holding $p$ fixed and finite. We find that the horizon dynamics of black holes in large D can be recast into a well-posed initial value problem of dynamics of a non gravitational co-dimension one membrane propagating in flat space. The dynamical degrees of freedom of this membrane are its shape function and a divergence free velocity field. We find the equation of motion governing the dynamics of this membrane upto first subleading order in $\frac{1}{D-3}$.