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arXiv · 2410.11956

A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality

Harvey S. Reall
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Abstract

It has recently been proved that a third law of black hole mechanics does not hold for Einstein-Maxwell theory coupled to a massless charged scalar field: there exist solutions that describe gravitational collapse to form an exactly extremal Reissner-Nordstr\"om black hole in finite time. In this paper it is proved that such solutions do not exist in theories with matter fields satisfying a local mass-charge inequality. In such a theory, if a 2-surface has the same metric, extrinsic curvature, and Maxwell field as a cross-section of an extremal Reissner-Nordstr\"om horizon then this surface cannot have a compact interior and so cannot be a horizon cross-section of a black hole formed in gravitational collapse. This result is proved using spinorial techniques, which are also used to prove a mass-charge inequality for a modified version of the Dougan-Mason quasi-local mass.

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Harvey S. Reall. 2024-10-15. A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality. https://arxiv.org/abs/2410.11956

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