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

Abstract

In this work, we investigate the influence of the Lorentz symmetry breaking in the gravitational bending angle for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a nonzero 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. We also study the bending angle of massive particles, where we systematize the Ishihara method for its application in Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider three backgrounds. Two of them are asymptotically flat and were found by Bertolamy et al and Casana et al. The third was found very recently by Maluf et al and is not asymptotically flat due to an effective cosmological constant.I.

Traversable Casimir Wormholes in D Dimensions

“…We obtained an analytical expression for the shape function for D arbitrary (7). It reproduces the expressions found for D = 3 [2] and D = 4 [1], in addition to being asymptotically null.…”

“…To compute the redshift function we use the EoS (4) and the shape function (7) to write the Eq. (2b) in the compact form…”

“…General Relativity, proposed by Albert Einstein in 1915, seeks to describe the gravitational interaction as a geometric effect of spacetime in response to a source of matter [3,4]. Over the years it has proved to be very assertive, ensuring predictability of various phenomena [5][6][7][8]. Even in 1916, Karl Schwarzschild found the first non-trivial analytical solution for Einstein's equation, which describes the gravitational influence of a localized spherically symmetric matter [9].…”

Hamiltonian formulation of an effective modified gravity with nondynamical background fields

“…References [66][67][68] give an account of a scenario of an antisymmetric two-tensor acquiring a vacuum expectation value. Papers have also been written on black-hole solutions in the presence of bumblebee-type Lorentz violation [69][70][71][72][73]. Note that spontaneous Lorentz violation was demonstrated to occur in open-string field theory, too [7][8][9][10][11].…”

Superradiant instability of the Kerr-like black hole in Einstein-bumblebee gravity

“…R.Casana et al obtained an exact Schwarzschild-like solution in 2018 [9]. Then, the light deflection [10][11][12] and quasinormal modes [13] of this black hole have been addressed. Moreover, spherically symmetric black hole solutions with cosmological constant [14], global monopole [15], or Einstein-Gauss-Bonnet term [16] have also been found.…”