Exact Schwarzschild-like solution in a bumblebee gravity model

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.

Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking

“…which is the same as that in Ref. [10]. The metric (3.25) represents a purely radial Lorentz-violating black hole solution with rotating angular momentum a.…”

“…Seeking for black hole solutions are very important works in any theory of gravity, because black holes provide into the quantum gravity realm. In 2018, R. Casana et al found an exact Schwarzschild-like solution in this bumblebee gravity model and investigated its some classical tests [10]. However, rotating black hole solutions are the most relevant subcases for astrophysics.…”

Modified black hole solution with a background Kalb–Ramond field

“…That property differs the LSB KR black hole from the bumblebee black hole found in Ref. [11] whose (Schwarzschild) horizon is kept unchanged. In Ref.…”

“…(18) differs from the the Lorentz invariant KR solution [17] and from the LSB bumblebee black hole solutions in Ref. [11] and Ref. [12].…”

“…The pseudo-fields E µ and B µ are spacelike, i.e., E µ u µ = B µ u µ = 0. Thus, the KB VEV yields two background vector instead of only one produced by the bumblebee vev [11].…”