New Exact Vacuum Solutions in Extended Bumblebee Gravity

TL;DR

This paper explores new exact vacuum solutions in a generalized bumblebee gravity model with non-minimal couplings, revealing a richer solution space including black holes, wormholes, and naked singularities, and analyzing their thermodynamics.

Contribution

It introduces a set of up to ten exact solutions in a non-minimally coupled vector-tensor gravity model, expanding the known solution space and thermodynamic properties.

Findings

Diverse solutions including naked singularities, black holes, and wormholes are found.

Some black hole solutions exhibit zero entropy.

The variation of the action and vacuum expectation value constraints are non-commutative.

Abstract

We investigate the static spherically symmetric vacuum solutions in a generalized bumblebee gravity model characterized by non-minimal couplings $B^2 R$ and $B^\mu B^\nu R_{\mu\nu}$. We demonstrate that the variation of the action and the imposition of the vacuum expectation value constraint are non-commutative, leading to a richer solution space than previously explored. A diverse set of solutions, including naked singularities, black holes, and wormholes, is obtained, and as many as ten exact solutions are presented. The thermodynamic properties of the new black hole solutions are also analyzed, and a subset of these solutions is found to have zero entropy. We argue that if such a non-minimally coupled vector-tensor gravity provides a fundamental description of the universe, it is best described by a Bumblebee-type theory, where the vector field acquires a VEV.