Conservative second-order gravitational self-force on circular orbits and the effective one-body formalism

2016/03/30 by Donato Bini, Thibault Damour · 2 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Circular orbit #Classical mechanics #Computation #Cosmology and Gravitation Theories #Galaxy #Gravitation #Gravitational potential #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Omega #Order (exchange) #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Redshift #gr-qc

paper · pdf · doi:10.1103/physrevd.93.104040

18 pages, revtex4-1 macros used

arxiv created 2016/03/30 · openalex publication_date 2016/05/23 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider Detweiler's redshift variable z for a nonspinning mass m₁ in circular motion (with orbital frequency \mathrm\ensuremathΩ) around a nonspinning mass m₂. We show how the combination of effective-one-body (EOB) theory with the first law of binary dynamics allows one to derive a simple, exact expression for the functional dependence of z on the (gauge-invariant) EOB gravitational potential u=(m₁+m₂)/R. We then use the recently obtained high-post-Newtonian(PN)-order knowledge of the main EOB radial potential A(u;\ensuremathν) [where \ensuremathν=m₁m₂/(m₁+m₂)²] to decompose the second-self-force-order contribution to the function z(m₂\mathrm\ensuremathΩ,m₁/m₂) into a known part (which goes beyond the 4PN level in including the 5PN logarithmic term and the 5.5PN contribution) and an unknown one [depending on the yet unknown, 5PN, 6PN,…, contributions to the O(\ensuremathν²) contribution to the EOB radial potential A(u;\ensuremathν)]. We apply our results to the second-self-force-order contribution to the frequency shift of the last stable orbit. We indicate the expected singular behaviors, near the lightring, of the second-self-force-order contributions to both the redshift and the EOB A potential. Our results should help both in extracting information of direct dynamical significance from ongoing second-self-force-order computations and in parametrizing their global strong-field behaviors. We also advocate computing second-self-force-order conservative quantities by iterating the time-symmetric Green-function in the background spacetime.

Citations

• Second-order gravitational self-force
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries
• Testing gravity to second post-Newtonian order: A field-theory approach
• Effective one-body approach to general relativistic two-body dynamics
• Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry

Cited by

• On the foundations of general relativistic celestial mechanics
• Redshift Factor and the First Law of Binary Black Hole Mechanics in Numerical Simulations

Related

• Fourth post-Newtonian effective one-body dynamics
• Constants of motion in gravitational self-force theory
• High-order comparisons between post-Newtonian and perturbative self forces
• Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime