Geometrized effective-one-body formalism for extreme-mass-ratio limits: Generic orbits

Abstract

Compact objects inspiraling into supermassive black holes, known as extreme-mass-ratio inspirals, are an important source for future space-borne gravitational-wave detectors. When constructing waveform templates, usually the adiabatic approximation is employed to treat the compact object as a test particle for a short duration, and the radiation reaction is reflected in the changes of the constants of motion. However, the mass of the compact object should have contributions to the background. In the present paper, employing the effective-one-body formalism, we analytically calculate the trajectories of a compact object around a massive Kerr black hole with generally three-dimensional orbits and express the fundamental orbital frequencies in explicit forms. In addition, by constructing an approximate "constant" similar to the Carter constant, we transfer the dynamical quantities such as energy, angular momentum, and the "Carter constant" to the semilatus rectum, eccentricity, and orbital inclination with mass-ratio corrections. The linear mass-ratio terms in the formalism may not be sufficient for accurate waveforms, but our analytical method for solving the equations of motion could be useful in various approaches to building waveform models.

22 pages, 18figures

References in corpus (21)

• An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
• Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• On the final spin from the coalescence of two black holes
• A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Binary black hole merger in the extreme mass ratio limit
• Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
• Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
• A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
• Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Spinning test-body orbiting around a Kerr black hole: circular dynamics and gravitational-wave fluxes
• Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit
• Excitation of high frequency voices from intermediate-mass-ratio inspirals with large eccentricity

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• Energy flux and waveforms by coalescing spinless binary system in effective one-body theory
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• Analytical solutions of bound timelike geodesic orbits in effective-one-body frame