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

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

2007-07-30

arxiv.org/abs/0707.4420v2

Class.Quant.Grav.24:6025-6040,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages; minor corrections

Scientific paper

10.1088/0264-9381/24/23/022

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.

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