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 (18)

• Modeling the dynamics of tidally-interacting binary neutron stars up to merger
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• 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
• Tidal invariants for compact binaries on quasi-circular orbits
• Exploring tidal effects of coalescing binary neutron stars in numerical relativity II: Longterm simulations
• On finding fields and self-force in a gauge appropriate to separable wave equations
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential
• Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions
• Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approach
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals

Cited by in corpus (8)

• Black hole perturbation theory and gravitational self-force
• Evolution of small-mass-ratio binaries with a spinning secondary
• Self-Force Calculations with a Spinning Secondary
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
• New metric reconstruction scheme for gravitational self-force calculations
• Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations