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Minimum mass, maximum charge, and hyperbolicity in scalar Gauss-Bonnet gravity

Dario Rossi1,2,*, Leonardo Gualtieri1,2,†, and Thomas P. Sotiriou3,4,5,‡

  • 1Dipartimento di Fisica, Università di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
  • 2INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
  • 3Nottingham Centre of Gravity, Nottingham NG7 2RD, United Kingdom
  • 4School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 5School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *Contact author: dario.rossi@phd.unipi.it
  • †Contact author: leonardo.gualtieri@unipi.it
  • ‡Contact author: thomas.sotiriou@nottingham.ac.uk
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Phys. Rev. D 114, 064042 – Published 9 September, 2026

DOI: https://doi.org/10.1103/2qq5-cqzx

Abstract

We study the loss of hyperbolicity of perturbation equations for black hole solutions of scalar Gauss-Bonnet gravity. We consider a class of coupling functions allowing for static black hole solutions with arbitrary small masses. For masses below a minimum value, such solutions become unphysical, because the perturbation equations become elliptic; this arguably corresponds to the loss of validity of the effective field theory. We analyze the dependence of this minimum mass on the parameters of the theory, finding that with an appropriate choice of the coupling function, such mass can be chosen arbitrarily small. However, this does not correspond to larger deviations from general relativity, since observable quantities like the black hole scalar charge are bounded by above.

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Phys. Rev. D 114, 064042– Published 9 September, 2026
  • Received 23 April 2026
  • Accepted 22 July 2026
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