# Overcharging a multi black hole system and cosmic censorship

## TL;DR

This paper investigates whether overcharging a multi black hole system can produce a naked singularity, testing the cosmic censorship hypothesis through a generalized Wald experiment.

## Contribution

It extends Wald's overcharging experiment to multi black hole systems, demonstrating the robustness of cosmic censorship in these scenarios.

## Key findings

- Test particles cannot overcharge the system to produce a naked singularity.
- Supports the validity of cosmic censorship in multi black hole configurations.
- Provides a non-trivial example reinforcing cosmic censorship in four-dimensional GR.

## Abstract

We study the generalization of the gadenken 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 non-trivial example that supports the validity of the cosmic censorship hypothesis in four-dimensional general relativity.