Scattering effects of bumblebee gravity in metric-affine formalism

In this work, we explore a Schwarzschild-like black hole within the framework of metric-affine bumblebee gravity. First, we investigate the behavior of the Kretschmann scalar and singularities in this modified gravity approach. Next, we introduce a newly defined time coordinate related to a stationary asymptotically flat spacetime. We also analyze the scattering effects and numerically calculate and comprehensively examine the partial and total absorption cross sections. At the high-frequency approximation, we find that the absorption cross section tends to the geodesic capture cross section. The continued fraction method is applied to investigate the quasinormal modes, and we explore the deviations of both the real and imaginary terms of the quasinormal modes from the Schwarzschild case in detail. We verify the relation between the shadow radius and the real part of the quasinormal frequencies at the eikonal limit within this modified gravity framework. Finally, we examine the energy emission rate.