Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

Abstract

We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. We emphasize the increase in \lq\lq transcendentality" of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $\zeta (3)$ (as well as the square of Euler's constant $\gamma$) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u=GM/(c^{2}r)$ leaves the weak-field domain $u\ll 1$ to enter the strong field domain $u=O(1)$.

arXiv comment13 pages; 1 eps figure. Revtex latex macros used

References in corpus (28)

• Effective one-body approach to general relativistic two-body dynamics
• Transition from inspiral to plunge in binary black hole coalescences
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Dimensional regularization of the gravitational interaction of point masses
• 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
• Testing gravity to second post-Newtonian order: a field-theory approach
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Mode sum regularization approach for the self-force in black hole spacetime
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• 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
• 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
• On the periods of some Feynman integrals
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion
• Knots and Numbers in ${\varphi }^4$ Theory to 7 Loops and Beyond
• 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
• High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Self-force Regularization in the Schwarzschild Spacetime
• A new analytical method for self-force regularization II. Testing the efficiency for circular orbits

Cited by in corpus (35)

• Black holes, gravitational waves and fundamental physics: a roadmap
• Self-force and radiation reaction in general relativity
• Modeling the dynamics of tidally-interacting binary neutron stars up to merger
• Fourth post-Newtonian effective one-body dynamics
• 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
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Tidal invariants for compact binaries on quasi-circular orbits
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Quasi-circular inspirals and plunges from non-spinning effective-one-body Hamiltonians with gravitational self-force information
• Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case
• On the four-loop static contribution to the gravitational interaction potential of two point masses
• Towards a gravitational self force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions
• Experimental mathematics meets gravitational self-force
• Spin-dependent two-body interactions from gravitational self-force computations
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• High-order Tail in Schwarzschild Space-time
• High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries
• Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Horizon Surface Gravity in Corotating Black Hole Binaries
• Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole
• Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background
• Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime
• Analytic Approximations in GR and Gravitational Waves
• Multipolar Particles in Helically Symmetric Spacetimes
• High-order comparisons between post-Newtonian and perturbative self forces