Black holes in a cubic Galileon universe

TL;DR

This paper explores black hole solutions within a subclass of Horndeski theory featuring a cubic Galileon term, revealing new scalar field configurations that modify black hole properties and introduce primary hair.

Contribution

It provides analytic and numerical black hole solutions in a shift-symmetric cubic Galileon universe, highlighting the role of scalar field velocity as primary hair.

Findings

Analytic 3D solutions similar to BTZ with scalar modifications

Multiple 4D black hole branches with different effective cosmological constants

Scalar field velocity acts as primary hair for black holes

Abstract

We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.