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

TL;DR

This paper explores the existence of hairy black hole solutions in dilatonic Einstein-Gauss-Bonnet theory with negative coupling coefficients, expanding the known parameter space where the no-hair theorem can be evaded.

Contribution

It introduces a new integral constraint that allows for hairy black hole solutions with negative Gauss-Bonnet coupling, extending previous results.

Findings

Hairy black holes exist with negative Gauss-Bonnet coefficient.

A new integral constraint enables these solutions.

The properties of the black holes are analyzed via the Gauss-Bonnet term.

Abstract

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. We construct the new integral constraint allowing the existence of the hairy solutions with the negative $\alpha$. Through this procedure, we expand the evasion of the no-hair theorem for hairy black hole solutions.