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Exploring the small mass limit of stationary black holes in theories with Gauss-Bonnet terms

Fernandes, Pedro G S; Mulryne, David J; Delgado, Jorge F M


Pedro G S Fernandes

David J Mulryne

Jorge F M Delgado


In this work we examine the small mass limit of black holes (BHs), with and without spin, in theories where a scalar field is non-minimally coupled to a Gauss-Bonnet (GB) term. First, we provide an analytical example for a theory where a static closed-form solution with a small mass limit is known, and later use analytical and numerical techniques to explore this limit in standard scalar-GB theories with dilatonic, linear and quadratic-exponential couplings. In most cases studied here, we find an inner singularity that overlaps with the event horizon of the static BH as the small mass limit is reached. Moreover, since solutions in this limit possess a non-vanishing Hawking temperature, a naked singularity is expected to be reached through evaporation, raising questions concerning the consistency of these theories altogether. On the other hand, we provide for the first time in this context an example of a coupling where the small mass limit is never reached, thus preferred from the point of view of cosmic censorship. Finally, we consider BHs with spin and numerically investigate how this changes the picture, using these to place the tightest upper bounds to date on the coupling constant for the dilatonic and linear theories, with α ‾ < 1 km.


Fernandes, P. G. S., Mulryne, D. J., & Delgado, J. F. M. (2022). Exploring the small mass limit of stationary black holes in theories with Gauss-Bonnet terms. Classical and Quantum Gravity, 39(23), Article 235015.

Journal Article Type Article
Acceptance Date Nov 2, 2022
Online Publication Date Nov 14, 2022
Publication Date Dec 1, 2022
Deposit Date Jan 3, 2023
Publicly Available Date Jan 3, 2023
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Peer Reviewed Peer Reviewed
Volume 39
Issue 23
Article Number 235015
Keywords Paper, scalarization, Hawking evaporation, scalar-Gauss–Bonnet, small mass limit, scalar hair, black hole, modified gravity
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