Charged spherically symmetric black holes in scalar-tensor Gauss-Bonnet gravity

TL;DR

This paper introduces a new class of charged black hole solutions in scalar-tensor Gauss-Bonnet gravity, revealing unique properties such as higher-order electric fields, non-reducibility to Reissner-Nordström solutions, and varied horizon structures.

Contribution

The work presents novel four-dimensional black hole solutions with scalar fields in Gauss-Bonnet gravity coupled to electromagnetism, highlighting their distinct features and stability characteristics.

Findings

Black holes exhibit higher-order electric fields due to scalar coupling.

Solutions have softer singularities compared to Schwarzschild or Reissner-Nordström.

Black holes possess three horizons in AdS and two in dS space-times.

Abstract

We derive a novel class of four-dimensional black hole solutions in Gauss-Bonnet gravity coupled with a scalar field in presence of Maxwell electrodynamics. In order to derive such solutions, we assume the ansatz $ g_{tt}\neq g_{rr}{}^{-1}$ for metric potentials. Due to the ansatz for the metric, the Reissner Nordstr\"om gauge potential cannot be recovered because of the presence of higher-order terms ${\cal O}\left(\frac{1}{r}\right)$ which are not allowed to be vanishing. Moreover, the scalar field is not allowed to vanish. If it vanishes, a function of the solution results undefined. For this reason, the solution cannot be reduced to a Reissner Nordstr\"om space-time in any limit. Furthermore, it is possible to show that the electric field is of higher-order in the monopole expansion: this fact explicitly comes from the contribution of the scalar field. Therefore, we can conclude that the Gauss-Bonnet scalar field acts as non-linear electrodynamics creating monopoles, quadrupoles, etc. in the metric potentials. We compute the invariants associated with the black holes and show that, when compared to Schwarzschild or Reissner-Nordstr\"om space-times, they have a soft singularity. Also, it is possible to demonstrate that these black holes give rise to three horizons in AdS space-time and two horizons in dS space-time. Finally, thermodynamic quantities can be derived and we show that the solution can be stable or unstable depending on a critical value of the temperature.