Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits

Abstract

Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Post-geodesic effects include the gravitational self force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is $\mathcal{O}(S)$ out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits and show how the small body's spin shifts the frequencies ${\Omega }_r$ and ${\Omega }_{\varphi }$ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations. (Abridged)

38 pages, 5 figures, submitted to Physical Review D; corrected typo in Equation (C6)

References in corpus (34)

• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• Can environmental effects spoil precision gravitational-wave astrophysics?
• Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• A Periodic Table for Black Hole Orbits
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• Effective potentials and morphological transitions for binary black-hole spin precession
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Motion of spinning test bodies in Kerr spacetime
• Dynamics of Extended Spinning Masses in a Gravitational Field
• Forced motion near black holes
• Evolution of small-mass-ratio binaries with a spinning secondary
• Self-Force Calculations with a Spinning Secondary
• Growth of resonances and chaos for a spinning test particle in the Schwarzschild background
• Spinning test-body orbiting around a Kerr black hole: circular dynamics and gravitational-wave fluxes
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Chaos and Order in Models of Black Hole Pairs
• Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism
• Astrophysically relevant bound trajectories around a Kerr black hole
• Flip-flopping binary black holes
• Innermost stable circular orbits of charged spinning test particles
• Spin supplementary conditions for spinning compact binaries
• Tidal Dynamics in Kerr Spacetime
• Spin-geodesic deviations in the Schwarzschild spacetime
• Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
• Time parameterizations and spin supplementary conditions of the Mathisson-Papapetrou-Dixon equations
• Spin-geodesic deviations in the Kerr spacetime
• Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole
• Quadrupole effects on the motion of extended bodies in Kerr spacetime
• Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III: Spin-orbit coupling revisited
• Perturbation Method for Classical Spinning Particle Motion: I. Kerr Space-Time
• Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling
• An Analytic Perturbation Approach for Classical Spinning Particle Dynamics