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Violation of the Third Law of Black Hole Mechanics in Vacuum Gravity

John R. V. Crump*, Maxime Gadioux†, Harvey S. Reall‡, and Jorge E. Santos§

  • *Contact author: jrvc2@cam.ac.uk
  • †Contact author: mjhg2@cam.ac.uk
  • ‡Contact author: hsr1000@cam.ac.uk
  • §Contact author: jss55@cam.ac.uk
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Phys. Rev. Lett. 136, 171405 – Published 1 May, 2026

DOI: https://doi.org/10.1103/gbg1-pjgq

Abstract

We demonstrate numerically the existence of solutions of five-dimensional vacuum gravity describing the formation, in finite time, of an extremal rotating black hole from a preexisting Schwarzschild black hole. This is the first example of a violation of the third law of black hole mechanics in vacuum gravity and demonstrates that the third law is false independently of any matter model. We also demonstrate the existence of solutions describing the formation, in finite time, of an extremal rotating black hole from vacuum initial data that do not contain a black hole.

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Phys. Rev. Lett. 136, 171405– Published 1 May, 2026
  • Received 11 February 2026
  • Accepted 2 April 2026
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