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

TL;DR

This paper derives an exact Kerr-like black hole solution in Einstein-bumblebee gravity with spontaneous Lorentz symmetry breaking and analyzes how Lorentz violation affects the black hole shadow, potentially observable with future gravitational detectors.

Contribution

It provides the first exact Kerr-like solution in Einstein-bumblebee gravity and studies the impact of Lorentz violation on black hole shadows.

Findings

Lorentz breaking constant affects the radius of unstable spherical orbits.

Lorentz violation accelerates shadow distortion.

Shifts in shadow properties are similar to Einstein-aether black holes.

Abstract

We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to those of Einstein-aether black hole. The effect of the LV parameter on the black hole shadow is that it accelerates the appearance of shadow distortion, and could be detected by the new generation of gravitational antennas.