On Lovelock galileons and black holes

TL;DR

This paper explores black hole solutions in a scalar-tensor Lovelock theory with galileon interactions, revealing regular solutions with self-tuning properties and analyzing their behavior in different dimensions.

Contribution

It extends Boulware-Deser solutions to include galileon fields, demonstrating regular scalar fields on horizons and analyzing effects of time dependence in various dimensions.

Findings

Hairy black hole solutions with regular scalar fields.

Self-tuning properties for cosmological constant and Gauss-Bonnet coupling.

Solutions in higher dimensions are close to GR away from the horizon.

Abstract

We study a scalar-tensor version of Lovelock theory with a non trivial higher order galileon term involving the coupling of the Lovelock two tensor with derivatives of the scalar galileon field. For a static and spherically symmetric spacetime we extend the Boulware-Deser solution to the presence of a Galileon field. The hairy solution has a regular scalar field on the black hole event horizon and presents certain self tuning properties for the bulk cosmological constant and the Gauss-Bonnet coupling. The combined time and radial dependence of the galileon field permits its horizon regularity. Furthermore in order to investigate the effects of linear time dependence we find spherically symmetric solutions in 4 and 5 spacetime dimensions. They are shown to have singular horizons. Afar from the Schwarzschild radius and for weak higher dimensional couplings the solutions are perturbratively close to GR representing GR like star solutions for scalar tensor theories.