Expanded evasion of the black hole no-hair theorem in dilatonic Einstein-Gauss-Bonnet theory

Understand

We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is non-minimally coupled to the dilaton field.

• Hairy black holes with spherical symmetry seem to be easily constructed with a positive Gauss-Bonnet coefficient $\alpha$ within the coupling function, $f(\phi) = \alpha e^{\gamma \phi}$, in an asymptotically flat spacetime, i.e., no-hair theorem seems to be easily evaded in this theory.
• Therefore, it is natural to ask whether this construction can be expanded into the case with the negative coefficient $\alpha$.
• In this paper, we present numerically the dilaton black hole solutions with a negative $\alpha$ and analyze the properties of GB term through the aspects of the black hole mass.