Ergodic Hysteresis of the Kerr black hole spectrum

Abstract

We uncover a cascade of exceptional points (EPs) in the quasinormal mode spectrum of massive scalar perturbations of Kerr black holes, revealing an intricate non-Hermitian structure underlying their linear response. The cascade originates from a single damped mode that enters the extremal spectrum for sufficiently large field masses. We obtain evidence for an infinite sequence of EPs in the $(\ell ,m)=(1,1)$ and $(2,2)$ sectors near the extremal limit, mediating the transition between damped and zero-damping modes. Each EP carries a geometric phase that enables adiabatic mode mixing across the entire overtone spectrum, a phenomenon we refer to as adiabatic ergodicity.

v3: 10 pages, 5 figures, 3 tables. Revised to match published version; results unchanged

References in corpus (29)

• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Slow relaxation of rapidly rotating black holes
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Branching of quasinormal modes for nearly extremal Kerr black holes
• Irregular Liouville correlators and connection formulae for Heun functions
• Turbulent Black Holes
• WKB analysis of the Regge-Wheeler equation down in the frequency plane
• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate
• Resolving the topology of encircling multiple exceptional points
• Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Transient Instability of Rapidly Rotating Black Holes
• Resonant Excitation of Quasinormal Modes of Black Holes
• Perturbative connection formulas for Heun equations
• Quantum vacuum excitation of a quasi-normal mode in an analog model of black hole spacetime
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• Teukolsky master equation and Painlevé transcendents: numerics and extremal limit
• Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
• Dynamical encircling exceptional point in largely detuned multimode optomechanical system
• Exceptional point and hysteresis in perturbations of Kerr black holes
• Quasinormal modes and excitation factors of Kerr black holes
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• Expansions for semiclassical conformal blocks
• Black hole quasinormal mode resonances
• Complete quasinormal modes of Type-D black holes