Charged superradiant instability of spherically symmetric regular black holes in de Sitter spacetime: time- and frequency-domain analysis

We investigate the superradiant instability of Ayón-Beato–García–de Sitter (ABG-dS) black holes under charged scalar field perturbations, employing both time-domain evolutions and frequency-domain computations. We demonstrate that the instability manifests exclusively for the spherically symmetric mode with =0 ℓ = 0 for both massless and massive scalar field perturbations. In contrast, asymptotically flat ABG black holes remain stable in the massless limit, a finding that highlights the crucial role of the cosmological horizon in providing a confining boundary. We further analyze the dependence of the instability growth rate on the cosmological constant Λ Λ , the black hole charge Q , the scalar field charge q , and the scalar field mass μ μ . We find that the growth rate peaks at intermediate values of Λ Λ and q , and increases monotonically with Q . Conversely, an increase in the scalar field mass μ μ suppresses the instability, eventually quenching it when μ μ is sufficiently large. Compared with Reissner–Nordström–de Sitter black holes, ABG-dS black holes exhibit distinct instability characteristics, which arise from the modified electrostatic potential induced by nonlinear electrodynamics.