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

Chikun Ding,A Cavalcante,Changqing Liu,R Casana

doi:10.1140/epjc/s10052-020-7743-y

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.

Highlights

For the nature of spacetime, there is a most important principle: Lorentz invariance(LI), which is a pillar of general relativity (GR) and the standard model(SM) of particle physics which are both successful field theories describing universe
LI should not be an exact symmetry at all energies [3], when one considering quantum gravity effect, it should not be applicable
Though both GR and SM based on LI and the background of spacetime, they handle their entities in profoundly different manners

Summary

Introduction

For the nature of spacetime, there is a most important principle: Lorentz invariance(LI), which is a pillar of general relativity (GR) and the standard model(SM) of particle physics which are both successful field theories describing universe. The former describes gravitation at the classical level, and the latter depicts particles and other three fundamental interactions at the quantum level. The study of Lorentz violation (LV) is a valuable tool to probe the foundations of modern physics These studies include LV in the neutrino sector [5], the standard-model extension (SME) [6,7,8], LV in the non-gravity sector [9,10,11], and LV effect on the formation of atmospheric showers [12].

Einstein-bumblebee theory

Exact Kerr-like solution in Einstein-bumblebee model

Black hole shadow