https://doi.org/10.1140/epjc/s10052-024-12516-z
Regular Article - Theoretical Physics
No scalar-haired Cauchy horizon theorem in charged Gauss–Bonnet black holes
Center for Quantum Spacetime, Sogang University, 121-742, Seoul, Korea
Received:
2
October
2023
Accepted:
2
February
2024
Published online:
19
February
2024
Recently, a “no inner (Cauchy) horizon theorem” for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (
) black holes, as in the case without GB term. On the other hand, for the non-planar (
) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a “no-go theorem” for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions.
© The Author(s) 2024
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