Charged Superradiant Instability of Spherically Symmetric Regular Black Holes in de Sitter Spacetime: Time- and Frequency-Domain Analysis

TL;DR

This study analyzes the superradiant instability of Ayón-Beato-García-de Sitter black holes under massless charged scalar perturbations using time-domain and frequency-domain methods. It demonstrates that instability occurs exclusively for the l=0 mode due to confinement by the cosmological horizon, and that asymptotically flat ABG black holes remain stable in the massless limit. The growth rate depends nontrivially on the cosmological constant, scalar charge, and black hole charge, with a maximum at intermediate Λ and q and a monotonically increasing trend with Q, and it differs from the RN-dS case because nonlinear electrodynamics modifies the electrostatic potential. These results highlight the role of nonlinear electrodynamics in shaping stability properties in de Sitter backgrounds and may help distinguish regular from singular black holes in cosmological settings.

Abstract

We investigate the superradiant instability of Ayón-Beato-García-de Sitter (ABG-dS) black holes under massless charged scalar perturbations using both time-domain evolutions and frequency-domain computations. We show that the instability occurs only for the spherically symmetric mode with $\ell=0$, whereas asymptotically flat ABG black holes remain stable in the massless limit, which underscores the essential role of the cosmological horizon in providing a confining boundary. We further study the dependence of the growth rate on the cosmological constant $Λ$, the scalar charge $q$, and the black hole charge $Q$, finding that it reaches a maximum at intermediate values of $Λ$ and $q$ and increases monotonically with $Q$. Compared with Reissner-Nordström-de Sitter black holes, ABG-dS black holes exhibit distinct instability characteristics due to the modified electrostatic potential induced by nonlinear electrodynamics.

Figures (7)

• Figure 1: Left: Profile of the metric function $f(r)$ for various $\Lambda$, with $Q=0.3$. Right: Allowed region in the $Q-\Lambda$ plane for which the metric describes a black hole. The two critical curves $r_-=r_h$ and $r_h = r_c$ correspond to the two extremal limits.
• Figure 2: Left: Time evolution of the massless scalar field perturbations $\varphi \equiv \Psi/r$ for various $\Lambda = 10^{-\lambda}$. Right: Profiles of the corresponding effective potential $V_{I} (r)$. We set $Q=0.4, q=0.5$ and $\ell=0$. In the present case, instability only occurs when $\lambda \gtrsim 2.06$ and peaks at $\lambda \simeq 2.58$. All quantities are measured in units of $M$.
• Figure 3: Time evolution of the massless scalar field perturbations $\varphi \equiv \Psi/r$ for various $Q$ and $q$. We set $\Lambda=10^{-3}$ and $\ell=0$. In the left panel, we fix $q=0.5$. In the right panel, we fix $Q=0.4$ and the divergence rate of $|\varphi|$ peaks at $q \simeq 0.82$. All quantities are measured in units of $M$.
• Figure 4: Left: Time evolution of the massless scalar field perturbations $\varphi \equiv \Psi/r$ for various $\ell$. Right: Profiles of the corresponding effective potential $V_{I} (r)$. We set $\Lambda=10^{-3}, Q=0.4$ and $q=0.5$. All quantities are measured in units of $M$.
• Figure 5: Fundamental modes as a function of $\Lambda \equiv 10^{-\lambda}$. Here we set $Q=0.4, q=0.5$ and $\ell=0$. All quantities are measured in units of $M$.