Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order

Abstract

Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post-Newtonian (pN) expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around a Schwarzschild black hole. We extract coefficients up to 20pN order from numerical results that are calculated with an accuracy greater than 1 part in $10^{500}$. These results can be used to calibrate parameters in effective-one-body models of compact binaries, specifically the spin-orbit part of the effective Hamiltonian and the dynamically significant tidal part of the main radial potential of the effective metric. Our calculations are performed in a radiation gauge, which is known to be singular away from the particle. To overcome this irregularity, we define suitable Detweiler-Whiting singular and regular fields in this gauge, and we devise a rigorous mode-sum regularization method to compute the invariants constructed from the regular field.

References in corpus (47)

• Effective one-body approach to general relativistic two-body dynamics
• The motion of point particles in curved spacetime
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Self-force via a Green's function decomposition
• Analytic black hole perturbation approach to gravitational radiation
• Gravitational self force in extreme mass-ratio inspirals
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
• Modeling the dynamics of tidally-interacting binary neutron stars up to merger
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Mode sum regularization approach for the self-force in black hole spacetime
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Second-order gravitational self-force
• Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion
• Gravitational self force and gauge transformations
• Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Second Order Gravitational Self-Force
• Gravitational Self-force in a Radiation Gauge
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations
• EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Gravitational self-torque and spin precession in compact binaries
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Gravitational self-force from radiation-gauge metric perturbations
• Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order
• A practical, covariant puncture for second-order self-force calculations
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Gravitational radiation reaction and second order perturbation theory
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Tidal invariants for compact binaries on quasi-circular orbits
• Exploring tidal effects of coalescing binary neutron stars in numerical relativity II: Longterm simulations
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• On finding fields and self-force in a gauge appropriate to separable wave equations
• Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure
• Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approach
• Experimental mathematics meets gravitational self-force
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• Self-force from reconstructed metric perturbations: numerical implementation in Schwarzschild spacetime

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