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

Abstract

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 non-electromagnetic contribution to the stressenergy tensor of the matter satisfies the null energy condition. We then analyze the gedanken experiments proposed by Hubeny and others to over-charge and/or over-spin an initially slightly non-extremal 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, δ 2 M , which allows us to prove that no gedanken experiments of the generalized Hubeny type can ever succeed in over-charging and/or over-spinning a Kerr-Newman black hole, provided only that the non-electromagnetic 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 δ 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.2

Thermodynamics with pressure and volume under charged particle absorption

“…conducted on the conjecture for not only black holes of Einstein's theory of gravity, but also anti-de Sitter (AdS), lower-dimensional, and higher-dimensional black holes [18][19][20][21][22][23][24][25][26][27][28][29][30]. From a thermodynamic point of view, the conjecture is quite consistently related to the laws of thermodynamics.…”

Static charged Gauss-Bonnet black holes cannot be overcharged by the new version of gedanken experiments

“…In this paper, following the setup of the gedanken experiments proposed by Sorce and Wald [27], we investigated the weak cosmic censorship conjecture in EMGB gravity under the perturbation of the spherically charged infalling matter collision. First of all, based on the Iyer-Wald formalism, we derived the perturbation inequality under the second-order approximation when the matter fields satisfy the null energy condition.…”

“…Following a similar setup with [27], here we consider the case where the background geometry is a nearly extremal black hole which satisfies r m = (1 − ε)r h with some small parameter ε chosen to agree with the first-order perturbation of the matter source. Then, Eq.…”

Investigating the gedanken experiment to destroy the event horizon of a regular black hole

“…In this section, following the discussion in [26], we would like to derive the first two order perturbation inequalities for the static electrically regular black holes. Since the Lagrangian cannot be expressed explicitly, below we only consider the off-shell variation of the Lagrangian of the Einstein part, i.e.,…”