A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910774916546560 |
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| author | Reall, Harvey S. |
| author_facet | Reall, Harvey S. |
| contents | 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-Nordström 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-Nordström 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality Reall, Harvey S. General Relativity and Quantum Cosmology High Energy Physics - Theory 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-Nordström 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-Nordström 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. |
| title | A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.11956 |