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

Abstract

We study the scalar perturbations of asymptotically flat extremal Reissner-Nordström black holes via the quantum Seiberg-Witten geometry of $\mathcal{N}=2$ SU(2) gauge theory with $N_f=2$ flavors. The radial master equation, governed by a double confluent Heun equation, is exactly mapped to the quantum Seiberg-Witten curve, providing an exact quantization condition derived from the non-perturbative Nekrasov-Shatashvili free energy. Analytically, this exact dictionary unveils precise gauge-theoretic interpretations for critical physical thresholds, demonstrating that the superradiance and mass decoupling limits naturally reduce the master equation to the Whittaker equation and the reduced doubly confluent Heun equation (the latter corresponds to the SW geometry of the $\mathcal{N}=2$ SU(2) gauge theory with $N_f=1$), respectively. At the strict extremal limit, the coalescence of horizons induces a topological singularity that complicates the spectral analysis. By accommodating this irregular singularity, our geometric framework resolves the singularity coalescence and enables the extraction of the discrete global quasinormal mode. As our main contribution, we provide the first non-perturbative evaluation of the quasinormal modes spectrum for simultaneously charged and massive scalar fields directly at strict extremity. Furthermore, our analytical results reproduce numerical benchmarks for both neutral and charged massless probes, and naturally capture quasi-resonance behaviors.

arXiv comment29 pages, 9 tables, 1 figure; v2: new results added, including charged scalar cases and special limits discussions; v3: typos corrected, published version

References in corpus (38)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Quasinormal modes of black holes and black branes
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Quasi-Normal Modes of Stars and Black Holes
• Quasinormal modes of black holes: from astrophysics to string theory
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supersymmetric Yang-Mills Systems And Integrable Systems
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• Integrability and Seiberg-Witten Exact Solution
• Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
• Testing the no-hair theorem with GW150914
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Spectroscopy of Kerr black holes with Earth- and space-based interferometers
• Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (I) Inspiral-Merger
• Gravitational quasinormal radiation of higher-dimensional black holes
• Massive quasi-normal mode
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Classical Conformal Blocks and Painleve VI
• Matone's Relation in the Presence of Gravitational Couplings
• Quasinormal modes of maximally charged black holes
• Quasinormal modes of black holes and Borel summation
• How instanton combinatorics solves Painlevé VI, V and III's
• Massive charged scalar field in a Reissner-Nordstrom black hole background: quasinormal ringing
• Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Quasinormal modes of extremal black holes
• Quasinormal modes of charged fields around a Reissner-Nordström black hole
• Quasinormal modes of Kerr-de Sitter black holes via the Heun function
• Quasinormal Modes of C-metric from SCFTs
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• The extremal Reissner-Nordström black holes: an exact charged scalar quasiresonance
• Duality between Seiberg-Witten Theory and Black Hole Superradiance
• Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory