TY - JOUR

T1 - Finite-distance gravitational deflection of massive particles by a Kerr-like black hole in the bumblebee gravity model

AU - Li, Zonghai

AU - Övgün, Ali

N1 - Publisher Copyright:
© 2020 American Physical Society.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1/22

Y1 - 2020/1/22

N2 - In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak-field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically nonflat due to the existence of a bumblebee vector field. Thus, the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray, and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. In particular, we correct a mistake in the previous literature. Furthermore, we consider the finite-distance correction for the deflection angle of massive particles.

AB - In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak-field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically nonflat due to the existence of a bumblebee vector field. Thus, the deflection angle is modified and can be divided into three parts: the surface integral of the Gaussian curvature, the path integral of a geodesic curvature of the particle ray, and the change in the coordinate angle. In addition, we also obtain the same results by defining the deflection angle. The effects of the Lorentz breaking constant on the gravitational lensing are analyzed. In particular, we correct a mistake in the previous literature. Furthermore, we consider the finite-distance correction for the deflection angle of massive particles.

UR - http://www.scopus.com/inward/record.url?scp=85078730401&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.101.024040

DO - 10.1103/PhysRevD.101.024040

M3 - Article

AN - SCOPUS:85078730401

SN - 2470-0010

VL - 101

JO - Physical Review D

JF - Physical Review D

IS - 2

M1 - 024040

ER -