Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation

Abstract

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars ${\Psi }_0$ and ${\Psi }_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.

33 pages, 2 figures, 1 table

References in corpus (42)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• Resummation of Massive Gravity
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Horndeski theory and beyond: a review
• Matter and Antimatter in the Universe
• Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
• Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory
• Non-Spinning Black Holes in Alternative Theories of Gravity
• Testing the black hole "no-hair" hypothesis
• Nonlinearities in Black Hole Ringdowns
• Nonlinear effects in black hole ringdown
• Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
• Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes
• Improved gravitational-wave constraints on higher-order curvature theories of gravity
• Higher-Derivative Corrected Black Holes: Perturbative Stability and Absorption Cross-Section in Heterotic String Theory
• Probing Fundamental Physics with Gravitational Waves: The Next Generation
• Quasi-normal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: the first order in rotation
• Gravitational ringing of rotating black holes in higher-derivative gravity
• Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity
• Perturbations and quasi-normal modes of black holes in Einstein-Aether theory
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Gravitational spectrum of black holes in the Einstein-Aether theory
• Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric
• Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers
• Numerical computation of second order vacuum perturbations of Kerr black holes
• Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity
• Black Hole Gravitational Waves in the Effective Field Theory of Gravity
• Quasi-normal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: the second order in rotation
• Extreme mass-ratio inspirals around a spinning horizonless compact object
• An approach to computing spectral shifts for black holes beyond Kerr
• Analytical computation of quasi-normal modes of slowly-rotating black-holes in dCS gravity
• Are Parametrized Tests of General Relativity with Gravitational Waves Robust to Unknown Higher Post-Newtonian Order Effects?
• New metric reconstruction scheme for gravitational self-force calculations
• Polarization modes of gravitational waves in Quadratic Gravity
• Quasinormal ringing of black holes in Einstein aether theory
• Numerical Black Hole Solutions in Modified Gravity Theories: Axial Symmetry Case
• Petrov Type, Principal Null Directions, and Killing Tensors of Slowly-Rotating Black Holes in Quadratic Gravity
• Semi-analytic expressions for quasinormal modes of slowly rotating Kerr black holes
• Gravitational quasinormal modes of black holes in Einstein-aether theory
• Regular second order perturbations of binary black holes: The extreme mass ratio regime
• How Do Spherical Black Holes Grow Monopole Hair?

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• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Systematic biases due to waveform mismodeling in parametrized post-Einsteinian tests of general relativity: The impact of neglecting spin precession and higher modes
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• Ringdowns for black holes with scalar hair: the large mass case
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• Testing gravity with gauge-invariant polarization states of gravitational waves: Theory and pulsar timing sensitivity
• The ringdown of a black hole surrounded by a thin shell of matter
• Frequency contamination from new fundamental fields in black hole ringdowns
• Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
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• Axial Gravitational Perturbations of Slowly-Rotating Compact Objects in General Relativity and Beyond
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