Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations

Abstract

Understanding the orbits of spinning bodies in curved spacetime is important for modeling binary black hole systems with small mass ratios. At zeroth order in mass ratio, the smaller body moves on a geodesic. Post-geodesic effects are needed to model the system accurately. One very important post-geodesic effect is the gravitational self-force, which describes the small body's interaction with its own contribution to a binary's spacetime. Another post-geodesic effect, the spin-curvature force, is due to the smaller body's spin coupling to spacetime curvature. In this paper, we combine the leading orbit-averaged backreaction of point-particle gravitational-wave emission with the spin-curvature force to construct the worldline and gravitational waveform for a spinning body spiraling into a Kerr black hole. We use an osculating geodesic integrator, which treats the worldline as evolution through a sequence of geodesic orbits, as well as near-identity transformations, which eliminate dependence on orbital phases, allowing for fast computation of inspirals. The resulting inspirals and waveforms include all critical dynamical effects which govern such systems (orbit and precession frequencies, inspiral, strong-field gravitational-wave amplitudes), and as such form an effective first model for the inspiral of spinning bodies into Kerr black holes. We emphasize that our present calculation is not self consistent, since we neglect effects which enter at the same order as effects we include. However, our analysis demonstrates that the impact of spin-curvature forces can be incorporated into EMRI waveform tools with relative ease. The calculation is sufficiently modular that it should not be difficult to include neglected post-geodesic effects as efficient tools for computing them become available. (Abridged)

arXiv comment38 pages, including 17 pages of Appendices, 13 figures. Submitted to Physics Review D. This posting and submission supersedes arXiv:2305.08919, in response to helpful critical referee feedback

References in corpus (64)

• Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
• The construction and use of LISA sensitivity curves
• Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA
• Self-force and radiation reaction in general relativity
• Prospects for Fundamental Physics with LISA
• Model Waveform Accuracy Standards for Gravitational Wave Data Analysis
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Gravitational self force in extreme mass-ratio inspirals
• The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission
• Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
• Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
• Gravitational wave snapshots of generic extreme mass ratio inspirals
• Celestial mechanics in Kerr spacetime
• FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis
• Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
• Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Gravitational waveforms for compact binaries from second-order self-force theory
• Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Evolution of inspiral orbits around a Schwarzschild black hole
• Rotating black hole orbit functionals in the frequency domain
• Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
• Spacetime and orbits of bumpy black holes
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Transient resonances in the inspirals of point particles into black holes
• Gravitational self-force on generic bound geodesics in Kerr spacetime
• Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Highly eccentric inspirals into a black hole
• Enhancing the SEOBNRv5 effective-one-body waveform model with second-order gravitational self-force fluxes
• Forced motion near black holes
• Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion
• Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
• Evolution of small-mass-ratio binaries with a spinning secondary
• Fast Self-forced Inspirals
• Self-force corrections to the periapsis advance around a spinning black hole
• Importance of transient resonances in extreme-mass-ratio inspirals
• Self-Force Calculations with a Spinning Secondary
• Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime
• Hamilton-Jacobi equation for spinning particles near black holes
• Assessing the detectability of the secondary spin in extreme mass-ratio inspirals with fully-relativistic numerical waveforms
• Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
• Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case
• Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes
• Hamiltonians and canonical coordinates for spinning particles in curved space-time
• Second-order gravitational self-force in a highly regular gauge
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation
• Modeling transient resonances in extreme-mass-ratio inspirals
• Adiabatic equatorial inspirals of a spinning body into a Kerr black hole
• Complete set of quasi-conserved quantities for spinning particles around Kerr
• Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Highly eccentric EMRI waveforms via fast self-forced inspirals
• Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?
• Particle motion under the conservative piece of the self-force is Hamiltonian
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Nature Abhors a Circle

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• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane