On the smoothness of static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory

TL;DR

This paper investigates the smoothness properties of static multi-black hole solutions in higher-dimensional Einstein-Maxwell theory, revealing that such solutions generally lack smooth horizons and exhibit various degrees of differentiability issues.

Contribution

It demonstrates that multi-black hole solutions are less smooth than previously thought, with specific differentiability levels and singularities identified in higher dimensions.

Findings

In five dimensions, the metric is generically twice differentiable at the horizon.

In more than five dimensions, the metric is only once differentiable and has a curvature singularity.

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

Abstract

Previous work has shown that static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory do not possess smooth horizons. We show that the lack of smoothness is worse than previously demonstrated. We consider solutions describing multiple black holes on a common axis. In five dimensions, the metric is generically twice, but not three times, continuously differentiable at the horizon. The Maxwell field is generically continuous, but not differentiable, at the horizon. In more than five dimensions, the metric is once, but not twice, continuously differentiable, and there is a parallely-propagated curvature singularity at the horizon. The Maxwell field strength is again continuous, but not differentiable, at the horizon.