Thermal Ringdown of a Kerr Black Hole: Overtone Excitation, Fermi-Dirac Statistics and Greybody Factor

Abstract

We find a significant destructive interference among Kerr overtones in the early ringdown induced by an extreme mass-ratio merger of a massive black hole and a compact object, and that the ringdown spectrum apparently follows the Fermi-Dirac distribution. We numerically compute the spectral amplitude of gravitational waves induced by a particle plunging into a Kerr black hole and study the excitation of multiple quasi-normal (QN) modes. We find that the start time of ringdown is before the strain peak of the signal and corresponds to the time when the particle passes the photon sphere. When the black hole has the near-extremal rotation, the Kerr QN frequencies are close to the fermionic Matsubara frequencies with the Hawking temperature and the chemical potential of the superradiant frequency. We indeed find that the absolute square of the spectral amplitude apparently follows the Fermi-Dirac distribution with the chemical potential of around the real QN frequency of the fundamental mode. Fitting the Boltzmann distribution to the data in higher frequencies, the best-fit temperature is found out to be close to the Hawking temperature, especially for rapid rotations. In the near-extremal limit, the gravitational-wave spectrum exhibits a would-be Fermi degeneracy with the Fermi surface at the superradiant frequency $\omega ={\mu }_{\mathrm{H}}$. We show that the greybody factor, i.e., the absorption cross section of a black hole, leads to the Fermi-Dirac distribution. As the greybody factor is another no-hair quantity of black holes, this opens a new possibility that we can test general relativity by observationally searching for the Boltzmann distribution in $\omega \gtrsim {\mu }_{\mathrm{H}}$ without extracting QN modes from ringdown. We could measure the mass and angular momentum of ringing black holes and could probe the Kerr/CFT by measuring the greybody factor imprinted on the ringdown spectrum.

19 pages, 13 figures

References in corpus (33)

• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
• Observational Constraints on Black Hole Spin
• Nonlinearities in Black Hole Ringdowns
• Nonlinear effects in black hole ringdown
• Quasinormal ringing of Kerr black holes: The excitation factors
• Analysis of Ringdown Overtones in GW150914
• 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
• Ringdown overtones, black hole spectroscopy, and no-hair theorem tests
• Cargese Lectures on the Kerr/CFT Correspondence
• Greybody Factors and Charges in Kerr/CFT
• Branching of quasinormal modes for nearly extremal Kerr black holes
• Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones
• Spectroscopy of binary black hole ringdown using overtones and angular modes
• Nonlinear effects in the black hole ringdown: absorption-induced mode excitation
• The final twist: A model of gravitational waves from precessing black-hole binaries through merger and ringdown
• Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers
• Importance of mirror modes in binary black hole ringdown waveform
• Quasinormal modes and their overtones at the common horizon in a binary black hole merger
• High-overtone fits to numerical relativity ringdowns: beyond the dismissed n=8 special tone
• Modelling the Ringdown from Precessing Black Hole Binaries
• Asymptotic Spectroscopy of Rotating Black Holes
• Black hole spectroscopy horizons for current and future gravitational wave detectors
• Angular emission patterns of remnant black holes
• Frequency-Domain Analysis of Black-Hole Ringdowns
• Hidden conformal symmetry on the black hole photon sphere
• Universal features of gravitational waves emitted by superkick binary black hole systems
• Analyzing black-hole ringdowns
• Quasinormal Modes of Kerr Black Holes in Four and Higher Dimensions
• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Overtones, mirror modes, and mode-mixing in binary black hole mergers

Cited by in corpus (19)

• Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
• Correspondence between grey-body factors and quasinormal frequencies for rotating black holes
• Ringdown stability: greybody factors as stable gravitational-wave observables
• Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory
• Black hole perturbation theory and multiple polylogarithms
• Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes
• First few overtones probe the event horizon geometry
• Greybody Factors Imprinted on Black Hole Ringdowns. II. Merging Binary Black Holes
• Greybody factors, reflectionless scattering modes, and echoes of ultracompact horizonless objects
• Overtones of black holes via time-domain integration
• Slowly Decaying Ringdown of a Rapidly Spinning Black Hole: Probing the No-Hair Theorem by Small Mass-Ratio Mergers with LISA
• A Fermi Model of Quantum Black Hole
• Correspondence between quasinormal modes and grey-body factors in five-dimensional black holes
• Ringdown of a postinnermost stable circular orbit of a rapidly spinning black hole: Mass ratio dependence of higher harmonic quasinormal mode excitation
• Correspondence between quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes
• Korteweg-de Vries Integrals for Modified Black Hole Potentials: Instabilities and other Questions
• Greybody factors of charged black holes with axion hair
• Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
• Dynamical system approach to the spectral (in)stability of black holes under localised potential perturbations