An exact Schwarzschild-like solution in a bumblebee gravity model

TL;DR

This paper derives an exact Schwarzschild-like solution in a bumblebee gravity model with spontaneous Lorentz symmetry breaking and tests its observational consequences, setting stringent bounds on the model.

Contribution

It provides the first exact vacuum solution in a bumblebee gravity model and analyzes classical tests to constrain Lorentz symmetry breaking effects.

Findings

Established a Schwarzschild-like black hole solution.

Performed classical tests showing deviations due to Lorentz breaking.

Set upper bounds on Lorentz violation parameters at the 10^{-13} level.

Abstract

We have obtained an exact vacuum solution from a gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking, we have investigated some classics tests including the advance of the perihelion, bending of light and Shapiro's time-delay. Furthermore, we have computed some upper-bounds from which the most stringent one attains a sensitivity at the $10^{-13}$ level.