Constrain from shadows of $M87^*$ and $Sgr A^*$ and quasiperiodic oscillations of galactic microquasars on a black hole arising from metric-affine bumblebee model

Abstract: We examine a static spherically symmetric black hole metric that originates from the vacuum solution of the traceless metric-affine bumblebee model in which spontaneous Lorentz symmetry-breaking occurs when the bumblebee fields acquire a non-vanishing vacuum expectation value. A free Lorentz-violating parameter enters into the basic formulation of the metric-affine bumblebee model. In this study, we use observations from the Event Horizon Telescope (EHT) collaboration on $M87^*$ and $SgrA^*$ to analyse the shadow of the black hole and an attempt has been made to constrain that free Lorentz-violating parameter. We also investigate particle motion over time-like geodesics and compute the corresponding epicyclic frequencies. We further constrain the Lorentz-violating parameter by using the reported high-frequency quasi-periodic oscillations (QPOs) of microquasars, offering new insights into its possible impact on astrophysical phenomena.