Multi-centered Myers-Perry Black Holes in Five Dimensions

TL;DR

This paper introduces a new family of explicit multi-centered extremal rotating black hole solutions in five-dimensional vacuum gravity, demonstrating their regularity, horizon structure, and asymptotic properties, including a binary configuration with a bubble region.

Contribution

It provides the first explicit multi-centered extremal Myers-Perry black hole solutions in 5D, expressed via harmonic functions, with detailed analysis of their geometric and physical properties.

Findings

All centers have smooth $S^3$ horizons with rotation parameters $|j_i|<1/2

Curvature singularities are hidden behind horizons, no closed timelike curves outside horizons

Binary configuration shows no conical singularities, supported by an intermediate bubble

Abstract

We present a new family of multi-centered rotating black hole solutions in 5D vacuum Einstein gravity, providing explicit examples of cohomogeneity-three spacetimes. It is well known that, in the presence of two commuting Killing vector fields, the theory reduces to 3D gravity coupled to an $SL(3,\mathbb{R})$ nonlinear sigma model with five scalar fields. We show that the scalar fields of the extremal Myers-Perry solution can be expressed in terms of two harmonic functions on 3D flat space, and that promoting these functions to include multiple sources yields explicit multi-centered extremal Myers-Perry black holes located at arbitrary positions. Each center forms a smooth $S^3$ Killing horizon, provided that the rotation parameters satisfy $|j_i|<1/2$. We further demonstrate that all curvature singularities are hidden behind the horizons and that no closed timelike curves arise on or outside the horizons. The solutions are asymptotically locally Minkowski in the sense that constant-time hypersurfaces are asymptotically locally Euclidean (ALE). As a concrete example, we consider a binary configuration, examine its rod structure, and demonstrate the absence of conical singularities between the two black holes, indicating that they are supported by an intermediate bubble region separating them.