Extremal dyonic black holes in D=4 Gauss-Bonnet gravity

TL;DR

This paper studies extremal dyonic black holes in four-dimensional Gauss-Bonnet gravity coupled with dilaton and Maxwell fields, revealing how higher curvature corrections expand the parameter space and affect black hole entropy and solutions.

Contribution

It demonstrates that the Gauss-Bonnet term enlarges the allowed dilaton coupling range for dyon solutions and explores the impact on black hole entropy and asymptotic behaviors.

Findings

Gauss-Bonnet term extends the dilaton coupling parameter range for dyon solutions.

Black hole entropy interpolates between Bekenstein-Hawking and doubled values.

Existence of non-asymptotically flat dyon solutions approaching linear dilaton backgrounds.

Abstract

We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton (EMD) theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant $a$. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of $a$ to continuous domains in the plane $(a, q_m)$ the second parameter being the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordstr\"om solution but not to the extremal dyons of the EMD theory. Both solutions have the same values of the horizon radius as a function of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background.