Gedanken experiments to destroy a black hole. II. Kerr-Newman black holes cannot be overcharged or overspun

We consider gedanken experiments to destroy an extremal or nearly extremal Kerr-Newman black hole by causing it to absorb matter with sufficient charge and/or angular momentum as compared with energy that it cannot remain a black hole. It was previously shown by one of us that such gedanken experiments cannot succeed for test particle matter entering an extremal Kerr-Newman black hole. We generalize this result here to arbitrary matter entering an extremal Kerr-Newman black hole, provided only that the nonelectromagnetic contribution to the stress-energy tensor of the matter satisfies the null energy condition. We then analyze the gedanken experiments proposed by Hubeny and others to overcharge and/or overspin an initially slightly nonextremal Kerr-Newman black hole. Analysis of such gedanken experiments requires that we calculate all effects on the final mass of the black hole that are second-order in the charge and angular momentum carried into the black hole, including all self-force effects. We obtain a general formula for the full second order correction to mass, ${\ensuremath{\delta}}^{2}M$, which allows us to prove that no gedanken experiments of the generalized Hubeny type can ever succeed in overcharging and/or overspinning a Kerr-Newman black hole, provided only that the nonelectromagnetic stress-energy tensor satisfies the null energy condition. Our analysis is based upon Lagrangian methods, and our formula for the second-order correction to mass is obtained by generalizing the canonical energy analysis of Hollands and Wald to the Einstein-Maxwell case. Remarkably, we obtain our formula for ${\ensuremath{\delta}}^{2}M$ without having to explicitly compute self-force or finite size effects. Indeed, in an appendix, we show explicitly that our formula incorporates both the self-force and finite size effects for the special case of a charged body slowly lowered into an uncharged black hole.

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