Optical, Dynamic and Topological Characteristics of Deformed Schwarzschild Black Holes

We investigate the temperature, photon and shadow radii, quasinormal modes (QNMs), time domain profiles, greybody factors, emission rates and topological characteristics of deformed black holes, focusing on the effects of the deformation parameter $\alpha$ and control parameter $\beta$. Increasing $\alpha$ enhances the oscillation frequency and damping rate of gravitational waves, while $\beta$ shows non-linear behaviour. Electromagnetic perturbations exhibit similar trends, though with lower frequencies and damping rates. Greybody factors are mainly influenced by multipole moment $l$ and $\alpha$, with $\beta$ having a more subtle effect. These findings provide insights into black hole dynamics, mergers, and gravitational wave emissions.