An Iyer-Wald first law is established for general perturbations of Reissner-Nordstrom-de Sitter black holes, and a second-order Sorce-Wald argument shows that near-extremal such black holes cannot be overcharged under the null energy condition.
Electromagnetic field and cosmic censorship
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abstract
We construct a gedanken experiment in which an extremal Kerr black hole interacts with a test electromagnetic field. Using Teukolsky's solutions for electromagnetic perturbations in Kerr spacetime, and the conservation laws imposed by the energy momentum tensor of the electromagnetic field and the Killing vectors of the spacetime, we prove that this interaction cannot convert the black hole into a naked singularity, thus cosmic censorship conjecture is not violated in this case.
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The First Law and Weak Cosmic Censorship for de Sitter Black Holes
An Iyer-Wald first law is established for general perturbations of Reissner-Nordstrom-de Sitter black holes, and a second-order Sorce-Wald argument shows that near-extremal such black holes cannot be overcharged under the null energy condition.