Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization

Abstract

We study the neutral scalar perturbations of asymptotically flat extremal Reissner-Nordström black holes via the quantum geometry of $\mathcal{N}=2$ $\mathrm{SU(2)}$ gauge theory with $N_f=2$ flavors. The master equation, given by a double confluent Heun equation, is mapped to the quantum Seiberg-Witten curve in the Nekrasov-Shatashvili limit. We compute the quasinormal mode frequencies non-perturbatively using the quantization condition derived from the Nekrasov-Shatashvili free energy. Our analytical results accurately reproduce the numerical benchmarks for massless fields, and capture the quasi-resonance behavior of massive probes at the strict extremal limit.

Figures (1)

• Figure 1: The evolution of the fundamental QNM ($n=0, l=0$) for a neutral scalar field as a function of the dimensionless mass $m_p$ in the strict extremal RN limit ($Q=M$). The decay rate strictly approaches zero, explicitly illustrating the transition into the quasi-resonance regime.