Quasinormal frequencies for a black hole in a bumblebee gravity

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.