Constraining the metric-affine bumblebee gravity parameter using black hole shadows and quasiperiodic oscillations of galactic microquasars

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 $$M87^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:msup> <mml:mn>87</mml:mn> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> and $$SgrA^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>g</mml:mi> <mml:mi>r</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> 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.