Quasi--normal modes of the Ayón--Beato--García Black Hole surrounded by quintessence: Scalar field perturbations

TL;DR

Quasi-normal modes of a massless scalar field are studied for a regular black hole of the Ayon-Beato-Garcia type surrounded by quintessence, modeled via the Kiselev framework. The scalar perturbations reduce to a Schrödinger-type equation with an $f_{\omega_q}(r)$-dependent potential, and the spectrum is computed using the improved Asymptotic Iteration Method with a transformation $r=1/\xi$ to enforce the boundary conditions. The results show that the real part of the frequencies $\operatorname{Re}(\omega)$ increases with the ABG charge parameter $g^2$ while the damping $|\operatorname{Im}(\omega)|$ decreases with $g^2$, whereas increasing quintessence strength $c$ lowers both parts; frequencies are larger for $\omega_q=-4/9$ than for $-2/3$. These findings highlight how quintessence and nonlinear electrodynamics modify the QNM spectrum, with potential observational implications for gravitational-wave signals near dark-energy environments around regular black holes.

Abstract

We investigate the quasi--normal modes of a massless scalar field in the background of an Ayón--Beato--García black hole surrounded by quintessence, using the Asymptotic Iteration Method (AIM) with $30$ iterations. The results show that the real part of the frequencies increases with the charge parameter $g^2$, while the absolute value of the imaginary part decreases as $g^2$ 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, $ω_q =-2/3$ and $ω_q =-4/9$; however, the effects become more pronounced as $ω_q$ approaches $-1$. 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.

Figures (4)

• Figure 1: (a) The plot shows the behavior of $r_h$ as function of $g^2$ for $\omega_q = -2/3$ and $\omega_q = -4/9$. (b) The plot illustrates how $c$ varies with $g^2$ for the cases $\omega_q = -2/3$ and $\omega_q = -4/9$.
• Figure 2: (a) The behavior of the effective potential $V(r)$ is shown for various values of $g^2$, with $c = 0.05$ and $l = 2$. The solid line corresponds to $g^2 = 0.3$ and the dashed line to $g^2 = 0.1$. (b) The behavior of the effective potential $V(r)$ is shown for various values of $c$, with $g^2 = 0.1$ and $l = 2$. The solid line corresponds to $c = 0.01$ and the dashed line to $c = 0.06$.
• Figure 3: (a) The behavior of $\omega_r$ as a function of $c$ is shown for $\omega_q = -2/3$ and $\omega_q = -4/9$. (b) The behavior of $|\omega_i|$ as a function of $c$ is shown for the same values of $\omega_q$. In both cases, the other parameters are fixed at $g^2 = 0.1$ and $l = 2$. The solid line corresponds to $\omega_q = -2/3$, while the dashed line represents $\omega_q = -4/9$.
• Figure 4: (a) The behavior of $\omega_r$ as a function of $g^2$ is shown for $\omega_q = -2/3$ and $\omega_q = -4/9$. (b) The behavior of $|\omega_i|$ as a function of $g^2$ is shown for the same values of $\omega_q$. In both cases, the other parameters are fixed at $c= 0.05$ and $l = 2$. The solid line corresponds to $\omega_q = -2/3$, while the dashed line represents $\omega_q = -4/9$.