Quasi-normal modes of the Ay\'on-Beato-Garc\'ia black hole surrounded by quintessence

Abstract

We compute the quasi-normal modes of scalar, electromagnetic, and gravitational perturbations of an Ay\'on-Beato-Garc\'ia black hole surrounded by quintessence using the Asymptotic Iteration Method (30 iterations). The results are compared with the WKB approximation to evaluate the robustness and accuracy of AIM. The results show that the real part of the frequencies increases with the charge parameter, while the absolute value of the imaginary part decreases as the charge parameter increases. In contrast, both the real part and the absolute value of the imaginary part decrease as the quintessence parameter $c$ increases. These trends are observed for both values of the quintessence state parameter, $\omega_q=-2/3$ and $\omega_q=-4/9$; however, the effects become more pronounced as $\omega_q$ approaches $-1$ corresponding to cosmological constant. The quasi-normal frequencies tend to have finite values, which could facilitate their observational detection. Moreover, the presence of quintessence leads to a slower damping of the perturbations.