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Formation of extremal Reissner-Nordström black holes: Insights from numerics

Maxime Gadioux*, Harvey S. Reall†, and Jorge E. Santos‡

  • *Contact author: mjhg2@cam.ac.uk
  • †Contact author: hsr1000@cam.ac.uk
  • ‡Contact author: jss55@cam.ac.uk
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Phys. Rev. D 113, 084001 – Published 1 April, 2026

DOI: https://doi.org/10.1103/k4dn-j3s6

Abstract

An extremal Reissner-Nordström black hole can form in finite time in the gravitational collapse of a massless charged scalar field. The proof of this is based on the method of characteristic gluing, which involves making an Ansatz for the scalar field at the horizon. We perform a numerical investigation of the characteristic gluing procedure for several different Ansätze. In each case, gluing is possible only if the final black hole mass is large enough. We find that the minimum required mass varies significantly for different Ansätze. We also consider the effect of including a mass term for the scalar field. In this case, for each Ansatz we determine the maximum mass-to-charge ratio for the scalar field such that gluing is possible. Analogous results are obtained for a nonzero cosmological constant.

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Phys. Rev. D 113, 084001– Published 1 April, 2026
  • Received 28 January 2026
  • Accepted 12 March 2026
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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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