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

TL;DR

This paper analyzes the superradiant instability of regular black holes in de Sitter spacetime, revealing that instability occurs only for the spherically symmetric mode and depends on parameters like the cosmological constant and charge.

Contribution

It provides a detailed time- and frequency-domain analysis of the superradiant instability in ABG-dS black holes, highlighting the role of nonlinear electrodynamics and the cosmological horizon.

Findings

Instability occurs only for the spherically symmetric mode with ℓ=0.

Stability persists for asymptotically flat ABG black holes in the massless limit.

Growth rate depends on Λ, q, and Q, with maximum at intermediate values.

Abstract

We investigate the superradiant instability of Ay\'on-Beato-Garc\'ia-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 $\Lambda$, the scalar charge $q$, and the black hole charge $Q$, finding that it reaches a maximum at intermediate values of $\Lambda$ and $q$ and increases monotonically with $Q$. Compared with Reissner-Nordstr\"om-de Sitter black holes, ABG-dS black holes exhibit distinct instability characteristics due to the modified electrostatic potential induced by nonlinear electrodynamics.