The gravitational bending angle by static and spherically symmetric black holes in bumblebee gravity

¹ Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici Fortaleza, CE, C.P. 6030, 60455-760, Brazil
² International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário Lagoa Nova, Natal, RN 59078-970, Brazil
³ Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Departamento de Ensino, Campus Crateús 63700-000, Crateús, CE, Brazil

^(a) icarodias@alu.ufc.br (corresponding author)

Received: 12 April 2021
Accepted: 1 June 2021

Abstract

This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.