Black hole non-uniqueness via spacetime topology in five dimensions

TL;DR

This paper demonstrates that in five-dimensional spacetimes, the presence of non-trivial 2-cycles can lead to violations of black hole uniqueness, showing multiple solutions with identical conserved charges but different topologies.

Contribution

It introduces explicit examples of supersymmetric black holes with identical conserved charges but different topologies, highlighting non-uniqueness due to spacetime topology in five dimensions.

Findings

Existence of black holes with identical charges but different topologies.

Presence of non-trivial 2-cycles can violate black hole uniqueness.

A decoupling limit yields solutions with a black hole and an exterior 2-cycle.

Abstract

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior. We show there are black holes in this family with identical conserved changes to the BMPV black hole, thereby demonstrating black hole non-uniqueness in this context. We find a decoupling limit of this family of black holes that yields spacetimes asymptotic to the near-horizon geometry of a BMPV black hole which contain a black hole and an exterior 2-cycle.