Scalar/Dirac perturbations of the Reissner-Nordstr\"om black hole and Painlev\'e transcendents

TL;DR

This paper analyzes scalar and Dirac perturbations of Reissner-Nordström black holes using isomonodromic methods, computing quasinormal modes and exploring near-extremal limits, revealing non-damping modes and bifurcation points.

Contribution

It introduces a novel application of isomonodromic methods to compute quasinormal modes for charged black holes, including near-extremal cases, and identifies non-damping modes and bifurcation phenomena.

Findings

Computed quasinormal modes as functions of charge and mass ratios.

Identified non-damping modes above a critical charge value.

Located bifurcation points in the parameter space.

Abstract

We investigate spin-$0$ and spin-$\frac{1}{2}$ perturbations for non-extremal and extremal Reissner-Nordstr\"om backgrounds using the isomonodromic method. We calculate the fundamental quasinormal modes (QNMs) associated with each perturbation as a function of the electromagnetic coupling $qQ$ and ratio $Q/M$. After corroborating the literature values for generic $qQ$ and $Q/M$, we turn to study the near-extremal limit. In parallel with the study of QNMs for the Kerr geometry, we find the existence of "non-damping" modes for $qQ$ above a spin-dependent critical value, and locate the bifurcation point in the $q-Q$ parameter space.