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Regular black holes from pure gravity in four dimensions

Johanna Borissova1,* and Raúl Carballo-Rubio2,†

  • *Contact author: j.borissova@imperial.ac.uk
  • †Contact author: raul.carballorubio@iaa.csic.es
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Phys. Rev. D 113, 124004 – Published 2 June, 2026

DOI: https://doi.org/10.1103/6x2z-qbkh

Abstract

We derive static spherically symmetric regular black holes as vacuum solutions to purely gravitational theories in four dimensions. To that end, we construct four-dimensional nonpolynomial gravities starting from subclasses of two-dimensional Horndeski actions. By construction, these theories possess second-order equations of motion on spherically symmetric backgrounds. We show that a subset of these nonpolynomial gravities, referred to as nonpolynomial quasitopological gravities, admit single-function static spherically symmetric solutions whereby the metric function is determined by an algebraic equation. Solutions to these theories include the Hayward regular black-hole spacetime, for which a corresponding gravitational action is stated explicitly.

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Phys. Rev. D 113, 124004– Published 2 June, 2026
  • Received 9 March 2026
  • Accepted 29 April 2026
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