Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime

TL;DR

This paper explores Einstein-Gauss-Bonnet gravity coupled with a bumblebee field, revealing exact black hole and cosmological solutions, and demonstrating how the bumblebee field influences gravitational potential and black hole singularities.

Contribution

It provides new exact solutions in four-dimensional Einstein-Gauss-Bonnet gravity coupled to a bumblebee field, highlighting effects on black hole horizons and potential implications for dark energy.

Findings

Bumblebee field affects gravitational potential but not horizon location.

Black holes can be free from singularities if parameter  is large.

Gauss-Bonnet term influences late-time cosmological expansion.

Abstract

We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector. We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme. We also obtain a Schwarzschild-like bumblebee black hole solution in $D$-dimensional spacetime. We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential. That is, its gravitational potential has a minimum value(negative) in the black hole interior and has a positive value $1+\ell$ at short distance $r\rightarrow0$. If the constant $\ell$ is large enough, then this kind of black hole is practically free from the singularity problem. The thermodynamics and phase transition are also studied. In a cosmological context, it is interesting that the Gauss-Bonnet term has no effect on the conservation of energy equation. A late-time expansion of de Sitter universe can be replicated in an empty space. The Gauss-Bonnet term and the bumblebee field can both actually act as a form of dark energy.