Quasinormal frequencies for a black hole in a bumblebee gravity

Abstract

After recent observational events like the LIGO-Virgo detections of\ngravitational waves and the shadow image of M87* supermassive black hole by\nEvent Horizon Telescope (EHT), the theoretical study of black holes was\nsignificantly improved. Quantities as quasinormal frequencies, shadows, and\nlight deflection become more important to analyze black hole models. In this\ncontext, an interesting scenario to study is a black hole in the bumblebee\ngravity. The bumblebee vector field imposes a spontaneous symmetry breaking\nthat allows the field to acquire a vacuum expectation value that generates\nLorentz-Violating (LV) into the black hole. In order to compute the quasinormal\nmodes (QNMs) via the WKB method, we obtain the Reege-Wheeler's equation with a\nbell-shaped potential for this black hole. Both QNMs, the scalar and tensorial\nmodes, are computed for the black hole in the bumblebee scenario. Moreover, the\nstability of the Schwarzschild-like solution and some bounds to LV parameters\nare analyzed.\n