On the smoothness of the multi-BMPV black hole spacetime

TL;DR

This paper investigates the smoothness of the event horizon in multi-BMPV black hole spacetimes, revealing it is not fully smooth and analyzing the differentiability of the metric and fields at the horizon.

Contribution

It provides the first explicit demonstration of limited smoothness at the horizon in multi-BMPV black hole configurations, including rotating cases, and discusses effects of higher derivative terms.

Findings

The horizon is not twice differentiable in multi-BMPV black hole spacetimes.

The metric is once, but not twice, continuously differentiable at the horizon.

The Maxwell field strength is continuous but not differentiable at the horizon.

Abstract

We demonstrate that, in a multi-BMPV black hole spacetime, the event horizon is not smooth. We explicitly show that for a simpler configuration comprising a line of static extremal black holes and a single BMPV black hole, the metric at the horizon of the BMPV black hole is once, but not twice, continuously differentiable. We argue that this result is also valid when all the black holes are rotating. The Maxwell field strength is shown to be continuous, but not differentiable at the horizon. We also briefly demonstrate that previous work done to show lack of smoothness of static multi-centre solutions in five dimensions is not significantly modified by the inclusion of a higher derivative term in the action for five dimensional supergravity.