Gravitational traces of bumblebee gravity in metric–affine formalism

Abstract

This work explores various manifestations of bumblebee gravity within the metric--affine formalism. We investigate the impact of the Lorentz violation parameter, denoted as $X$, on the modification of the \textit{Hawking} temperature. Our calculations reveal that as $X$ increases, the values of the \textit{Hawking} temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the \textit{quasinormal} modes, we employ the WKB method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz--violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the \textit{quasinormal} spectrum on time--dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time--domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of $X$ correspond to larger shadow radii. Furthermore, we constrain the magnitude of the shadow radii using the EHT horizon--scale image of $Sgr A^*$. Finally, we calculate both the time delay and the deflection angle.