Overcharging a multi-black-hole system and cosmic censorship

We study the generalization of the gedanken experiment of overcharging an extremal black hole proposed by Wald in the context of a multi-black-hole solution. In particular, we attempt to overcharge a system of two extremal black holes via test particle absorption to produce a system involving a black hole and a naked singularity. If such a process is possible, then this would be a potential violation of the cosmic censorship hypothesis. However, we find that, analogous to Wald's result for a single charged black hole, such a test particle which can expose the singularity would not be able to enter the horizon. This provides an interesting and nontrivial example that supports the validity of the cosmic censorship hypothesis in four-dimensional general relativity.

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