Rotating Black Holes on Codimension-2 Branes

TL;DR

This paper derives exact solutions for small rotating black holes on codimension-2 branes with tension, revealing effects on black hole properties and the fundamental Planck scale in higher-dimensional models.

Contribution

It generalizes Schwarzschild solutions to include rotating black holes on tensioned codimension-2 branes, incorporating the effects of brane tension on black hole characteristics.

Findings

Brane tension resizes the fundamental Planck mass.

Black hole size and lifetime increase with tension.

Angular velocity varies depending on angular momentum orientation.

Abstract

It has recently been demonstrated that certain types of non-tensional stress-energy can live on tensional codimension-2 branes, including gravitational shockwaves and small Schwarzschild black holes. In this note we generalize the earlier Schwarzschild results, and construct the exact gravitational fields of small rotating black holes on a codimension-2 brane. We focus on the phenomenologically interesting case of a three-brane embedded in a spacetime with two compactified extra dimensions. For a nonzero tension on the brane, we verify that these solutions also show the ``lightning rod'' effect found in the Schwarzschild solutions, the net effect of which is to rescale the fundamental Planck mass. This allows for larger black hole parameters, such as the event horizon, angular momentum, and lifetime than would be naively expected for a tensionless brane. It is also found that a black hole with angular momentum pointing purely along the brane directions has a smaller horizon angular velocity than the corresponding tensionless case, while a hole with bulk components of angular momentum has a larger angular velocity.