Interaction of higher-dimensional rotating black holes with branes

TL;DR

This paper investigates how rotating higher-dimensional black holes interact with branes, showing they can lose certain angular momentum components and reach a stationary state where the horizon's null Killing vector aligns with the brane.

Contribution

It provides a general proof for the behavior of rotating black holes interacting with branes in higher dimensions, including the timescale to reach equilibrium.

Findings

Black holes can lose bulk angular momentum components.

Stationary black holes have angular momentum aligned with brane-preserving symmetries.

Characteristic relaxation time depends on black hole size, brane tension, and extra dimensions.

Abstract

We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can loose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher dimensional black holes interacting with branes. 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.