Static spherical vacuum solutions in the bumblebee gravity model

TL;DR

This paper explores static spherical vacuum solutions in the bumblebee gravity model, revealing two families of black-hole solutions with unique properties, and tests their observational viability.

Contribution

It introduces two new families of black-hole solutions in the bumblebee gravity model and analyzes their properties and observational implications.

Findings

Found two families of black-hole solutions with distinct vector field configurations.

Identified solutions with nonstandard horizon properties and finite curvature scalars.

Tested the solutions against Solar-system data and supermassive black hole images.

Abstract

The bumblebee gravity model is a vector-tensor theory of gravitation where the vector field nonminimally couples to the Ricci tensor. By investigating the vacuum field equations with spherical symmetry, we find two families of black-hole (BH) solutions in this model: one has a vanishing radial component of the vector field and the other has a vanishing radial component of the Ricci tensor. When the coupling between the vector field and the Ricci tensor is set to zero, the first family becomes the Reissner-Nordstr\"om solution while the second family degenerates to the Schwarzschild solution with the vector field being zero. General numerical solutions in both families are obtained for nonzero coupling between the vector field and the Ricci tensor. Besides BH solutions, we also reveal the existence of solutions that have a nonvanishing $tt$-component of the metric on the supposed event horizon where the $rr$-component of the metric diverges while the curvature scalars are finite. These solutions are not supported by existing observations but present certain properties that are of academic interests. We conclude the study by putting the BH solutions into tests against the Solar-system observations and the images of supermassive BHs.