Quasi-normal modes and absorption section from regular black holes immersed in perfect fluid dark matter

TL;DR

This work investigates how a perfect fluid dark matter (PFDM) environment modifies the dynamics of perturbations and scattering around three regular black-hole families (Hayward, Bardeen, ABG). By applying both the 6th-order WKB approximation and the asymptotic iteration method, it computes the quasi-normal modes and absorption cross sections for massless scalar and electromagnetic fields, with the horizon fixed at $r_+=1$ to study parameter dependencies. The results demonstrate dynamical stability (negative Im parts) and show that both the real part and the damping rate increase with the multipole number $l$, while PFDM via the intensity parameter $oldsymbol{ extalpha}$ and charges $q_i$ shift the spectra and cross sections, notably making the Bardeen case more absorbing. These findings suggest PFDM can imprint observable signatures on strong-gravity phenomena such as gravitational waves and black-hole shadows.

Abstract

We study scalar and electromagnetic perturbations of three families of regular black holes, Hayward, Bardeen, and Ayon-Beato-García immersed in a Perfect Fluid Dark Matter (PFDM) background. Using both the sixth-order WKB approximation and the Asymptotic Iteration Method (AIM), we determine the corresponding quasi-normal modes and absorption cross sections. By fixing the horizon radius , we analyze the dependence of the parameters of the black holes and the parameter of PFDM. The computed quasi-normal modes confirming the dynamical stability of the black holes under scalar and electromagnetic perturbations. Furthermore, both the real and imaginary parts of the quasi-normal modes increase with the multipole number $l$, corresponding to higher oscillation frequencies and faster damping rates. On the other hand absorption cross sections compared under similar parametric conditions. The results demonstrate that PFDM influences the dynamical properties of regular black holes.

Figures (5)

• Figure 1: a) The parametric region that allows the event horizon $r_+$ and inner horizon $r_-$. The region below the curves $h_1$ (for values ($\alpha,q_1^2$)), $h_2$ (for values ($\alpha,q_2^2$)) and $h_3$ (for values ($\alpha,q_3^2$)) have to two event horizons, while for all values ($\alpha,q_1^2$), ($\alpha,q_2^2$)), ($\alpha,q_3^2$)) where $h_1=0$, $h_2=0$ and $h_3=0$, the BHs have only one horizon $r_+$. b) The behaviour of the metric function for Hayward, Bardeen and AGB Black Holes. The solid lines are $\alpha=-0.1$ and $q_1^2=q_2^2=q_3^2 =0.1$, while the dotted lines are for $\alpha=-0.3$, $q_1^2=0.571789$, $q_2^2=0.575457$ and $q_3^2=0.406527$.
• Figure 2: a) The behavior of $V_s(r)$ with $r$ for scalar perturbations, where the solid line corresponds to $\alpha=-0.1$ and the dot-dashed line corresponds to $\alpha=-0.4$ Here $q_1^2=q_2^2=q_3^2=0.1$ and $l=1$. b) The behavior of the effective potential $V_s(r)$ is showed for different values of $q_1^2$, $q_2^2$ and $q_3^2$, with $\alpha=-0.1$ and $l=1$. The solid lines are for $q_1^2=q_2^2=q_3^2=0.1$, while the dot-dashed lines are for $q_1^2=q_2^2=q_3^2=0.3$.
• Figure 3: a) The behavior of $V_{em}(r)$ with $r$ for electromagnetic perturbations, where the solid line corresponds to $\alpha=-0.1$ and the dot-dashed line corresponds to $\alpha=-0.4$ Here $q_1^2=q_2^2=q_3^2=0.1$ and $l=1$. b) The behavior of the effective potential $V_{em}(r)$ is showed for different values of $q_1^2$, $q_2^2$ and $q_3^2$, with $\alpha=-0.1$ and $l=1$. The solid lines are for $q_1^2=q_2^2=q_3^2=0.1$, while the dot-dashed lines are for $q_1^2=q_2^2=q_3^2=0.3$.
• Figure 4: The behavior of total absorption cross section for a massless scalar field propagating in regular black hole surrounded by perfect fluid dark matter, with $\alpha=-0.2$. The summation in \ref{['ec.sata']} is performed up to $l=10$. In the left panel we use $q_1^2=q_2^2=q_3^2=0.2$, while in the right panel $q_1^2=q_2^2=q_3^2=0.1$.
• Figure 5: The behavior of total absorption cross section for a massless scalar field propagating in regular black hole surrounded by perfect fluid dark matter, with $q_{i}=0.15$. The summation in \ref{['ec.sata']} is performed up to $l=10$. In the left panel we use $\alpha= -0.1$, while in the right panel $\alpha=-0.3$.