Quasinormal frequencies for a black hole in a bumblebee gravity

Abstract

After recent observational events like the LIGO-Virgo detections of gravitational waves and the shadow image of the M87* supermassive black hole by event horizon telescope (EHT), the theoretical study of black holes was significantly improved. Quantities as quasinormal frequencies, shadows, and light deflection become more important to analyze black hole models. In this context, an interesting scenario to study is a black hole in the bumblebee gravity. The bumblebee vector field imposes a spontaneous symmetry breaking that allows the field to acquire a vacuum expectation value that generates Lorentz Violation (LV) into the black hole. In order to compute the quasinormal modes (QNMs) via the WKB method, we obtain the Reege-Wheeler's equation with a bell-shaped potential for this black hole. Both QNMs, the scalar and tensorial modes, are computed for the black hole in the bumblebee scenario. The results obtained in bumblebee gravity are compared to Schwarzschild and Einstein-aether black holes. In general, the LV parameter decreases the real part of frequency for scalar and gravitational perturbations. The modulus of imaginary parts is increased with the LV parameter for the scalar field and decreased by the gravitational field. Moreover, the time-domain perturbations are studied and damping profiles are shown.

Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

“…Several studies [57][58][59][60][61][62][63][64][65][66][67] have already been made to describe the observational implications of this bumblebee field and, thus, our results certainly provide a substantial contribution to this task.…”

“…The main reason is that our intent was basically to illustrate how the method can be applied, leaving their due analysis for future publications, especially because of the complexity most of them present. Concerning the simplest ones, which are the first two solutions, the second one provides essentially the same spacetime as the first, for which many studies have already been made [61][62][63][64][65][66][67]72,73]. Only the last example had a small further analysis with regard to its distinguished surfaces.…”

Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

“…The main reason is because our intent was basically to illustrate how the method can be applied, leaving their due analysis for future publications, especially in view of the complexity most of them present. Concerning the simplest ones, which are the first two solutions, the second one provides essentially the same spacetime as the first, for which many studies have already been made [61][62][63][64][65][66][67][68]. Only the last example had a small further analysis with regard to its distinguished surfaces.…”

Thermal Correction to the Kinnersley Black Hole in a Lorentz-Violating Dirac Field Theory

“…With research of string theory and quantum gravity theory, people have realized that the Lorentz relation should be modified at high energy, which will lead to the Dirac equation in curved space-time to be modified. The application of Lorentz-violating theory in curved space-time is a Frontier subject worthy of attention [34][35][36][37][38][39][40]. Cruz et al introduced the Lorentz symmetry violating term in the scalar field Lagrangian, namely the Lorentzviolating scalar field theory, to research thermal corrections to the Casimir energy [41].…”