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

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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.