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Supersymmetric black holes and the third law of black hole mechanics

Aidan M. McSharry* and Harvey S. Reall†

  • *Contact author: amm323@cam.ac.uk
  • †Contact author: hsr1000@cam.ac.uk
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Phys. Rev. D 112, 104009 – Published 6 November, 2025

DOI: https://doi.org/10.1103/s44z-rbzx

Abstract

Recently it has been shown that the third law of black hole mechanics can be violated; an exactly extremal Reissner-Nordström black hole can form in finite time in gravitational collapse of matter with a large charge to mass ratio. However, it has also been proved that this cannot happen if the matter satisfies a “supersymmetric” lower bound on its energy in terms of its charge. This paper proves an analogous result for black holes with a negative cosmological constant. The result states that a supersymmetric Kerr-Newman-anti–de Sitter black hole cannot form in gravitational collapse of charged matter satisfying the supersymmetric bound. The results for zero or negative cosmological constant are extended to apply to two-sided black holes; it is proved that an initially nonextremal black hole cannot evolve to a supersymmetric black hole in finite time, irrespective of whether or not the initial black hole was formed in gravitational collapse.

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Phys. Rev. D 112, 104009– Published 6 November, 2025
  • Received 29 July 2025
  • Accepted 3 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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