Rotating Black Holes which Saturate a Bogomol'nyi Bound

TL;DR

This paper constructs and analyzes electrically charged, rotating black hole solutions in heterotic string theory, revealing that for dimensions greater than five, extremal limits saturate the Bogomol'nyi bound, unlike the four-dimensional case.

Contribution

It introduces new rotating black hole solutions in heterotic string theory that saturate the Bogomol'nyi bound for higher dimensions, and explores their properties and superpositions.

Findings

For D > 5, extremal black holes saturate the Bogomol'nyi bound.

In D=4, solutions develop naked singularities before reaching the bound.

Superposing solutions in higher dimensions yields four-dimensional black holes without naked singularities.

Abstract

We construct and study the electrically charged, rotating black hole solution in heterotic string theory compactified on a $(10-D)$ dimensional torus. This black hole is characterized by its mass, angular momentum, and a $(36-2D)$ dimensional electric charge vector. One of the novel features of this solution is that for $D >5$, its extremal limit saturates the Bogomol'nyi bound. This is in contrast with the $D=4$ case where the rotating black hole solution develops a naked singularity before the Bogomol'nyi bound is reached. The extremal black holes can be superposed, and by taking a periodic array in $D>5$, one obtains effectively four dimensional solutions without naked singularities.