Exceptional point and hysteresis in perturbations of Kerr black holes

Abstract

We employ the isomonodromic method to study linear scalar massive perturbations of Kerr black holes for generic scalar masses $M\mu$ and generic black hole spins $a/M$. We find that the longest-living quasinormal mode and the first overtone coincide for $(M\mu {)}_c\simeq 0.3704981$ and $(a/M{)}_c\simeq 0.9994660$. We also show that the longest-living mode and the first overtone change continuously into each other as we vary the parameters around the point of degeneracy, providing evidence for the existence of a geometric phase around an exceptional point. We interpret our findings through a thermodynamic analogy.

arXiv commentv3: 8 pages, 4 figures. Typos corrected, figures updated, improved discussion

References in corpus (70)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• String Axiverse
• Exceptional Topology of Non-Hermitian Systems
• Quasinormal modes of black holes: from astrophysics to string theory
• Black Hole Entropy from Near-Horizon Microstates
• Thermodynamical Aspects of Gravity: New insights
• On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
• The Kerr/CFT Correspondence
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Kerr black holes with scalar hair
• Exploring the String Axiverse with Precision Black Hole Physics
• Non-Hermitian Topology and Exceptional-Point Geometries
• Stationary Black Holes: Uniqueness and Beyond
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Hawking Radiation and Black Hole Thermodynamics
• Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
• Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
• Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
• Spectroscopy of Kerr black holes with Earth- and space-based interferometers
• Overcharging a Black Hole and Cosmic Censorship
• Stationary Scalar Clouds Around Rotating Black Holes
• Over-spinning a black hole with a test body
• Classification of near-horizon geometries of extremal black holes
• Matched-filtering and parameter estimation of ringdown waveforms
• Black Hole Superradiance From Kerr/CFT
• Gedanken Experiments to Destroy a Black Hole II: Kerr-Newman Black Holes Cannot be Over-Charged or Over-Spun
• Superradiant instabilities of rotating black holes in the time domain
• Analysis of Ringdown Overtones in GW150914
• Weak Cosmic Censorship: As Strong as Ever
• Stability and quasinormal modes of the massive scalar field around Kerr black holes
• Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown
• Slow relaxation of rapidly rotating black holes
• Gravitational perturbations of the Kerr geometry: High-accuracy study
• Gravitational instability of an extreme Kerr black hole
• Classes of Exact Solutions to the Teukolsky Master Equation
• Branching of quasinormal modes for nearly extremal Kerr black holes
• Late-time dynamics of rapidly rotating black holes
• Quasinormal modes of maximally charged black holes
• Test fields cannot destroy extremal black holes
• How instanton combinatorics solves Painlevé VI, V and III's
• Overspinning a nearly extreme charged black hole via a quantum tunneling process
• A massive charged scalar field in the Kerr-Newman background I: quasinormal modes, late-time tails and stability
• The extremal black hole bomb
• Overtones or higher harmonics? Prospects for testing the no-hair theorem with gravitational wave detections
• Cosmic Censorship, Area Theorem, and Self-Energy of Particles
• What happens at the horizon(s) of an extreme black hole?
• Quasinormal modes of extremal black holes
• Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate
• Particle motion near high-spin black holes
• A superradiance resonance cavity outside rapidly rotating black holes
• Can quantum mechanics fool the cosmic censor?
• Gedanken experiments on nearly extremal black holes and the Third Law
• Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
• Heun equation, Teukolsky equation, and type-D metrics
• Irregular conformal blocks and connection formulae for Painlevé V functions
• Transient Instability of Rapidly Rotating Black Holes
• Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime
• The Collisional Penrose Process
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Semiclassical Decay of Near-Extremal Black Holes
• A note on the resonant frequencies of rapidly rotating black holes
• Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes
• Teukolsky master equation and Painlevé transcendents: numerics and extremal limit
• High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency
• Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• Expansions for semiclassical conformal blocks
• Estimate of the radius responsible for quasinormal modes in the extreme Kerr limit and asymptotic behavior of the Sasaki-Nakamura transformation

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