Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms

TL;DR

This paper investigates the small mass limit of black holes in scalar-Gauss-Bonnet theories, revealing singularities and potential violations of cosmic censorship, while identifying couplings that avoid these issues and constraining theory parameters.

Contribution

It provides the first example of a coupling where the small mass limit is avoided, and offers new bounds on coupling constants using spinning black holes.

Findings

Inner singularities overlap with horizons at small mass

Certain couplings prevent the small mass limit from being reached

Tightest bounds on coupling constants are established for spinning black holes

Abstract

In this work we examine the small mass limit of black holes, with and without spin, in theories where a scalar field is non-minimally coupled to a Gauss-Bonnet 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-Gauss-Bonnet 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 black hole 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 black holes 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 $\sqrt{\overline{\alpha}} < 1$ km.