Reissner-Nordstr\"om Black Holes on a Codimension-2 Brane

TL;DR

This paper derives an exact Reissner-Nordstr"om black hole solution on a codimension-2 brane, revealing how brane tension amplifies both gravitational and electric field strengths, extending previous Schwarzschild and Kerr results.

Contribution

It provides the first exact solution for a charged black hole on a codimension-2 brane, generalizing earlier uncharged solutions and demonstrating the effects of brane tension on electric fields.

Findings

Exact Reissner-Nordstr"om solution on a codimension-2 brane.

Brane tension amplifies the apparent strength of gravity and electric fields.

Extension of Schwarzschild and Kerr solutions to charged black holes.

Abstract

Here we derive the exact Reissner-Nordstr\"om black hole solution on a tensional codimension-2 brane, generalizing earlier Schwarzschild and Kerr results. We begin by briefly reviewing various aspects of codimension-2 branes that will be important for our analysis, including the mechanism of "offloading" of brane tension into the bulk that is unique to these branes, as well as the explicit construction of the codimension-2 Schwarzschild black hole as a warm-up exercise. We then show that the same methods can be used to find the metric describing the spacetime surrounding an electrically-charged point source threaded by a codimension-2 brane. The presence of the brane tension leads to an amplification of the apparent strength of gravity, as is well-known, and we further find exactly the same enhancement for the apparent strength of the electric field.