Anomalous decay rate of quasinormal modes in Reissner-Nordstr\"om black holes

TL;DR

This paper investigates the unusual decay rates of quasinormal modes in charged black holes, extending previous studies to Reissner-Nordström spacetimes and revealing how charge and scalar mass influence mode behavior.

Contribution

It extends the analysis of anomalous decay rates of quasinormal modes to charged black holes, identifying critical scalar masses and mode dominance patterns.

Findings

Anomalous decay rates occur in charged black holes' photon sphere modes.

Critical scalar mass increases with black hole charge, affecting decay behavior.

Mode dominance varies with black hole parameters and scalar mass.

Abstract

The anomalous decay rate of the quasinormal modes occurs when the longest-lived modes are the ones with higher angular number. Such behaviour has been recently studied in different static spacetimes, for scalar and fermionic perturbations, being observed in both cases. In this work, we extend the existent studies to the charged spacetimes, namely, the Reissner-Nordstr\"om, the Reissner-Nordstr\"om-de Sitter and the Reissner-Nordstr\"om-Anti-de Sitter black holes. We show that the anomalous decay rate behaviour of the scalar field perturbations is present for every charged geometry in the photon sphere modes, with the existence of a critical scalar field mass whenever $\Lambda \geq 0$. In general, this critical value of mass increases with the raise of the black hole charge, thus rendering a minimum in the Schwarzschild limit. We also study the dominant mode/family for the massless and massive scalar field in these geometries showing a non-trivial dominance of the spectra that depends on the black hole mass and charge.