Rotating Black Holes which Saturate a Bogomol'nyi Bound

TL;DR

This work constructs electrically charged, rotating black holes in heterotic string theory compactified on a torus and demonstrates that, in spacetime dimensions D>5, the extremal limit can saturate a Bogomol'nyi bound without developing naked singularities. Using solution-generating transformations on the higher-dimensional Kerr solution, the authors derive explicit D-dimensional metrics and fields, analyze horizon properties, and identify the extremal (BPS) regime via decomposed charges Q_L and Q_R. They further show that extremal holes can be superposed into multicenter and periodic-array configurations, yielding exact string backgrounds described by chiral null models and providing lower-dimensional analogs with matched gyromagnetic ratios to elementary string states. The results highlight the crucial role of dimensionality in BPS black holes and connect to string dualities, offering a framework for relating black hole microstates to string states through four-dimensional reductions.

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.