Rotating Yukawa-modified black holes: QNM and shadow studies

This study investigates the quasinormal modes (QNMs) and shadows of rotating black holes (BHs) with a Yukawa-type scalar field in Modified Gravity (MOG), also known as scalar-tensor-vector gravity (STVG), providing tests using data from Event Horizon Telescope (EHT) observations. The metric incorporates Yukawa-like corrections to the gravitational potential in MOG, characterized by parameters $\alpha$ (MOG field strength) and $\beta$ (Yukawa field exponent). We derive the corresponding rotating black hole solution, study the event horizon, ergoregion, static limit, and effective mass, analyzing their dependence on the black hole and gravity parameters. We calculated the photonsphere and shadow radii, and our analysis confirmed that increasing the black hole spin reduces the shadow size and increases the distortion. In contrast, the presence of MOG and Yukawa fields causes an increase in shadow size with constraints from EHT data on M87* and Sgr A*, yielding bounds like $\alpha <0.5$ and $\beta \approx 0.2$ at $2\sigma$ confidence for moderate spins. Furthermore, we study equatorial and polar QNMs using the geometric–optics correspondence between photon ring parameters and QNM frequencies, in order to assess the impact of the deformations. Energy emission rates via Hawking radiation are also studied, linking to the shadow radius. Results demonstrate deviations from Kerr, with EHT compatibility favoring small Yukawa and STVG modifications. These findings bridge theoretical predictions with observations, constraining alternative gravity models.