Strong lensing effect and quasinormal modes of oscillations of black holes in f(R,T) gravity theory

In this work, we analyze the strong lensing phenomenon and quasinormal modes (QNMs) in the case of black holes (BHs) surrounded by fluids within the framework of $f(R,T)$ gravity, adopting a minimally coupled model of the theory. Our analysis is conducted for three surrounding fields corresponding to three different values of the parameter $\omega$ of the equations of state, each representing a unique class of BH solutions. A universal method developed by V. Bozza is employed for strong lensing analysis and the WKB approximation method to compute the QNMs of oscillation of the BHs. The influences of the model parameters $\beta$ and $c_2$ on the deflection angle and associated lensing coefficients are analyzed. Our findings on lensing reveal that smaller values of $\beta$ and $c_2$ cause photon divergence at larger impact parameters as well as the lensing results converge to the Schwarzschild limit. Extending the analysis to the supermassive BH Sgr A*, we examine the outermost Einstein rings, estimate three lensing observables: angular position ${\vartheta }_{\infty }$, angular separation $s$ and relative magnification $r_{\text{mag}}$ for the BHs. For a specific values of $\beta$ and $c_2$, BHs with different field configurations exhibit substantial variations in their observable properties. The variation of amplitude and damping of QNMs with respect to the model parameter $\beta$ and $c_2$ is analyzed for the BHs. We found that the $\beta$ parameter has a direct correlation with the amplitude and an inverse relation with the damping of the QNMs, while $c_2$ has direct correlation with amplitude as well as damping. Further, we use the time domain analysis to verify the results and found a good match between the two methods.