Proof of the weak cosmic censorship conjecture for several extremal black holes
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Proof of the weak cosmic censorship conjecture for several extremal black holes Jéssica Gonçalves1 · José Natário2 Received: 17 April 2020 / Accepted: 27 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We show explicitly, for different types of extremal black holes, that test fields satisfying the null energy condition at the event horizon cannot violate the weak cosmic censorship conjecture. This is done by checking, in each case, that the hypotheses for a general theorem proved in a previous paper are satisfied. Keywords Weak cosmic censorship · Extremal black holes · Black hole thermodynamics · BTZ black holes · Quintessence · Gauss-Bonnet-AdS black holes · Nonlinear electrodynamics · Born–Infeld-AdS black holes · Stringy black holes · MTZ black holes
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Weak cosmic censorship conjecture . . . . . . . . . . . . . . . 3 BTZ black hole . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Quintessence RN-AdS black hole . . . . . . . . . . . . . . . . 5 Gauss–Bonnet-AdS black hole . . . . . . . . . . . . . . . . . . 6 RN-AdS black hole in nonlinear electrodynamics . . . . . . . . 7 BTZ black hole in nonlinear electrodynamics . . . . . . . . . . 8 Born–Infeld-AdS black holes . . . . . . . . . . . . . . . . . . 9 Charged toroidal black holes . . . . . . . . . . . . . . . . . . . 10 Charged black holes in string theory . . . . . . . . . . . . . . . 11 5D charged rotating minimally gauged supergravity black hole . 12 (2 + 1)-dimensional MTZ black holes . . . . . . . . . . . . . 13 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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José Natário [email protected]
1
School of Physics and Astronomy, University of Southampton, Southampton, UK
2
Mathematics Department, CAMGSD, IST, University of Lisbon, Lisbon, Portugal 0123456789().: V,-vol
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J. Gonçalves, J. Natário
1 Introduction In 1965, Penrose published the proof of the first singularity theorem [1], soon to be followed by increasingly more sophisticated results [2,3]. The singularities predicted by these theorems as a result of gravitational collapse do not need, in principle, to be hidden inside a black hole event horizon, that is, they could conceivably be naked singularities. This would signal a major breakdown of general relativity, as the physics
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