Tidal response and near-horizon boundary conditions for spinning exotic compact objects

Abstract

Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to in-going gravitational waves, respond to these waves, and generate out-going waves. As it also turns out, if both in-going and out-going waves exist near the horizon, the Newman Penrose (NP) quantity ${\psi }_0$ will be numerically dominated by the in-going wave, while the NP quantity ${\psi }_4$ will be dominated by the out-going wave. In this way, we obtain the ECO boundary condition in the form of a relation between ${\psi }_0$ and the complex conjugate of ${\psi }_4$, in a way that is determined by the ECO's tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame, and deduce the corresponding ECO boundary condition for Teukolsky functions. We subsequently obtain the boundary condition for ${\psi }_4$ alone, as well as for the Sasaki-Nakamura and Detweiler's functions. As it also turns out, reflection of spinning ECOs will generically mix between different $\ell$ components of the perturbations fields, and be different for perturbations with different parities. We also apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and solve for the spinning ECOs' quasi-normal modes.

arXiv comment20 pages, 6 figures

References in corpus (60)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Black Holes: Complementarity or Firewalls?
• Cool horizons for entangled black holes
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• The fuzzball proposal for black holes: an elementary review
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• Is the gravitational-wave ringdown a probe of the event horizon?
• Gravitational Vacuum Condensate Stars
• Black Hole Shadows, Photon Rings, and Lensing Rings
• Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale
• AdS/CFT duality and the black hole information paradox
• Better Late than Never: Information Retrieval from Black Holes
• Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons
• The observational evidence for horizons: from echoes to precision gravitational-wave physics
• Tests for the existence of horizons through gravitational wave echoes
• Analytic black hole perturbation approach to gravitational radiation
• The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
• Echoes of Kerr-like wormholes
• A recipe for echoes from exotic compact objects
• Gravitational wave echoes through new windows
• Gravitational wave echoes from black hole area quantization
• Tidal coupling of a Schwarzschild black hole and circularly orbiting moon
• How does a dark compact object ringdown?
• Tidal heating as a discriminator for horizons in extreme mass ratio inspirals
• Distinguishing fuzzballs from black holes through their multipolar structure
• Echoes from Quantum Black Holes
• A New Window into Black Holes
• Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
• Black hole ringdown echoes and howls
• Probing microstructure of black hole spacetimes with gravitational wave echoes
• Probing the nature of central objects in extreme-mass-ratio inspirals with gravitational waves
• Nonviolent unitarization: basic postulates to soft quantum structure of black holes
• On Reflectivity of Quantum Black Hole Horizons
• Black Holes Lessons from Multipole Ratios
• Astronomical tests for quantum black hole structure
• The multipolar structure of fuzzballs
• Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation
• Fuzzballs and Observations
• A generalization of Ryan's theorem: probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals
• Gravitational Wave "Echo" Spectra
• Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes III. Quasinormal Pulsations of Schwarzschild and Kerr Black Holes
• Effective Field Theory of Black Hole Echoes
• Searching for quantum black hole structure with the Event Horizon Telescope
• Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes
• Tidal heating of Quantum Black Holes and their imprints on gravitational waves
• Obstruction of black hole singularity by quantum field theory effects
• Stellar Black Holes and the Origin of Cosmic Acceleration
• How loud are echoes from exotic compact objects?
• Searching for near-horizon quantum structures in the binary black-hole stochastic gravitational-wave background
• Spicing up the recipe for echoes from exotic compact objects: orbital differences and corrections in rotating backgrounds
• High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency
• Damping of gravitational waves in 2-2-holes
• Echoes from corpuscular black holes
• Gravitational Wave Perturbations on a Kerr Background and Applications for Echoes
• Gravitational wave echoes induced by a point mass plunging to a black hole

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• Recognizing black holes in gravitational-wave observations: Challenges in telling apart impostors in mass-gap binaries
• Towards establishing the presence or absence of horizons in coalescing binaries of compact objects by using their gravitational wave signals
• Gravitational-wave echoes from numerical-relativity waveforms via space-time construction near merging compact objects
• Ringdown of Charged Compact Objects using Membrane Paradigm
• Gravitational radiation close to a black hole horizon: Waveform regularization and the out-going echo
• Recipes for computing radiation from a Kerr black hole using a generalized Sasaki-Nakamura formalism: Homogeneous solutions
• Tidal-heating/viscous dissipation correspondence in black holes and viscous compact objects
• Gravitational wave echoes search with combs
• Echoes from beyond: Detecting gravitational-wave quantum imprints with LISA
• On the Interaction between Ultralight Bosons and Quantum-Corrected Black Holes
• Signatures of Quantum Gravity in Gravitational Wave Memory
• Gravitational-wave echoes from spinning exotic compact objects: numerical waveforms from the Teukolsky equation
• Sub-atomic constraints on the Kerr geometry of GW150914
• Implications of the quantum nature of the black hole horizon on the gravitational-wave ringdown