https://doi.org/10.1140/epjc/s10052-020-7743-y
Regular Article - Theoretical Physics
Exact Kerr-like solution and its shadow in a gravity model with spontaneous Lorentz symmetry breaking
1
Department of Physics, Hunan University of Humanities, Science and Technology, Loudi, 417000, Hunan, People’s Republic of China
2
Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China
3
Departamento de Física, Universidade Federal do Maranhão, São Luís, Maranhão, 65080-805, Brazil
* e-mail: Chikun_Ding@huhst.edu.cn
** e-mail: dingchikun@163.com
Received:
27
January
2020
Accepted:
10
February
2020
Published online:
27
February
2020
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 
decreases with the Lorentz breaking constant 
, and increases with 
. 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.
© The Author(s), 2020
