Rotating black holes in brane worlds

TL;DR

This paper investigates the behavior of rotating higher-dimensional black holes interacting with branes in large extra dimension scenarios, revealing conditions for stationarity and estimating the timescale to reach equilibrium.

Contribution

It demonstrates that a rotating black hole's stationarity depends on the null Killing vector being tangent to the brane, and provides a formula for the timescale to reach this state.

Findings

Stationary black holes require the null Killing vector to be tangent to the brane.

The timescale to reach stationarity is proportional to $r_0^{p-1}/(G\sigma)$.

Rotating black holes can be stationary only under specific geometric conditions.

Abstract

We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that a rotating black hole attached to a brane can be stationary only if the null Killing vector generating the black hole horizon is tangent to the brane world-sheet. The characteristic time when a rotating black hole with the gravitational radius $r_0$ reaches this final stationary state is $T\sim r_0^{p-1}/(G\sigma)$, where $G$ is the higher dimensional gravitational coupling constant, $\sigma$ is the brane tension, and $p$ is the number of extra dimensions.