High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

Abstract

The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision. In this paper, we build upon earlier work to carry this comparison still further, by examining next-to-next-to-leading order contributions beyond the half integral 5.5PN conservative effect, which arise from terms to cubic and higher orders in the metric and its multipole moments, thus extending scrutiny of the post-Newtonian methods to one of the highest orders yet achieved. We do this by explicitly constructing tail-of-tail terms at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in the small mass ratio limit, and comparing directly with numerically and analytically computed terms in the self-force approach, obtained using solutions for metric perturbations in the Schwarzschild space-time, and a combination of exact series representations possibly with more typical PN expansions. While self-force results may be relativistic but with restricted mass ratio, our methods, valid primarily in the weak-field slowly-moving regime, are nevertheless in principle applicable for arbitrary mass ratios.

arXiv comment33 pages, no figure; minor corrections

References in corpus (34)

• The motion of point particles in curved spacetime
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Self-force via a Green's function decomposition
• Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• A Rigorous Derivation of Gravitational Self-force
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• Gravitational-wave tails of tails
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• The complete non-spinning effective-one-body metric at linear order in the mass ratio
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Mass, inertia and gravitation
• Motion in alternative theories of gravity
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion
• The self-consistent gravitational self-force
• Analytic Solutions of the Teukolsky Equation and their Properties
• Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Gravitational Self-force in a Radiation Gauge
• Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian
• 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
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Quadrupole-quadrupole gravitational waves
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• 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
• Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries

Cited by in corpus (20)

• Black holes, gravitational waves and fundamental physics: a roadmap
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Self-force and radiation reaction in general relativity
• Fourth post-Newtonian effective one-body dynamics
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order
• Logarithmic tail contributions to the energy function of circular compact binaries
• Second-order perturbation theory: the problem of infinite mode coupling
• The mass quadrupole moment of compact binary systems at the fourth post-Newtonian order
• Experimental mathematics meets gravitational self-force
• Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism
• Horizon Surface Gravity in Corotating Black Hole Binaries
• Analytic Approximations in GR and Gravitational Waves
• Multipolar Particles in Helically Symmetric Spacetimes
• First-post-Newtonian generation of gravitational waves in Einstein-Cartan theory