Quasinormal frequencies for a black hole in a bumblebee gravity

TL;DR

This paper investigates the quasinormal frequencies of a black hole in bumblebee gravity, revealing how Lorentz violation affects black hole oscillations and stability, with implications for gravitational wave observations.

Contribution

It introduces the calculation of quasinormal modes for a black hole in bumblebee gravity, incorporating Lorentz-violating effects and analyzing stability and parameter bounds.

Findings

Computed scalar and tensorial QNMs for the black hole in bumblebee gravity.

Analyzed stability of Schwarzschild-like solutions under Lorentz violation.

Provided bounds on Lorentz-violating parameters based on QNM analysis.

Abstract

After recent observational events like the LIGO-Virgo detections of gravitational waves and the shadow image of 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-Violating (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. Moreover, the stability of the Schwarzschild-like solution and some bounds to LV parameters are analyzed.