Long-Lived Quasinormal Modes of Brane-Localized Reissner-Nordstr\"om--de Sitter Black Holes

Abstract

We study the quasinormal modes of a massive scalar field propagating on the Reissner-Nordstr\"om--de Sitter (RNdS) black hole black hole background on a 3+1-dimensional brane embedded in a higher-dimensional world. Using the WKB method supplemented with Pad\'e approximants and validated by time-domain integration via the Prony method, we compute the dominant quasinormal frequencies for a wide range of black hole and field parameters. We show that the presence of the cosmological constant, black hole charge, and bulk dimensionality significantly affect the oscillation frequencies and damping rates of the scalar perturbations. In particular, we observe the emergence of long lived modes and slowly decaying oscillatory tails in the regime of large field mass. The results demonstrate good agreement between the frequency- and time-domain methods, reinforcing the reliability of the semi-analytic approach in this context.