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

Understand

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.