Scalar/Dirac perturbations of the Reissner-Nordstr\"om black hole and Painlev\'e transcendents
Abstract
We investigate spin-0 and spin-12 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.
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