Topological black holes for Einstein-Gauss-Bonnet gravity with a nonminimal scalar field

TL;DR

This paper constructs novel planar AdS black hole solutions in Einstein-Gauss-Bonnet gravity with a nonminimal scalar field, including stealth configurations and solutions with additional (D-1)-forms, highlighting the role of specific coupling constants.

Contribution

It introduces new classes of planar AdS black hole solutions with nonminimal scalar fields in Einstein-Gauss-Bonnet gravity, including stealth configurations and solutions with extra (D-1)-forms, under specific coupling conditions.

Findings

Two classes of AdS black hole solutions with planar horizons are derived.

Stealth scalar field solutions reduce to pure AdS when parameters vanish.

Adding (D-1)-forms allows black hole solutions with arbitrary nonminimal coupling.

Abstract

We consider the Einstein-Gauss-Bonnet gravity with a negative cosmological constant together with a source given by a scalar field nonminimally coupled in arbitrary dimension D. For a certain election of the cosmological and Gauss-Bonnet coupling constants, we derive two classes of AdS black hole solutions whose horizon is planar. The first family of black holes obtained for a particular value of the nonminimal coupling parameter only depends on a constant M, and the scalar field vanishes as M=0. The second class of solutions corresponds to a two-parametric (with constants M and A) black hole stealth configuration, that is a nontrivial scalar field with a black hole metric such that both side (gravity and matter parts) of the Einstein equations vanishes. In this case, in the vanishing M, the solution reduces to a stealth scalar field on the pure AdS metric. We note that the existence of these two classes of solutions is inherent of the particular choice of the coupling constants and, they can not be promoted to spherical or hyperboloid black hole solutions in a standard fashion. In the last part, we add to the original action some exacts (D-1)-forms coupled to the scalar field. The direct benefit of introducing such extra fields is to obtain black hole solutions with planar horizon for arbitrary value of the nonminimal coupling parameter.