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

Abstract

We consider Detweiler's redshift variable $z$ for a nonspinning mass $m_1$ in circular motion (with orbital frequency $\Omega$) around a nonspinning mass $m_2$. 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 $u=(m_1+m_2)/R$. We then use the recently obtained high-post-Newtonian(PN)-order knowledge of the main EOB radial potential $A(u;\nu )$ [where $\nu =m_1{m}_2/(m_1+m_2{)}^2$] to decompose the second-self-force-order contribution to the function $z(m_2\Omega ,m_1/m_2)$ 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, $\dots$, contributions to the $O({\nu }^2)$ contribution to the EOB radial potential $A(u;\nu )$]. 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.

18 pages, revtex4-1 macros used

References in corpus (21)

• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Fourth post-Newtonian effective one-body dynamics
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• 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
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Tidal invariants for compact binaries on quasi-circular 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
• Second-order gravitational self-force
• Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential
• New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole
• Analytic determination of high-order post-Newtonian self-force contributions to gravitational spin precession
• Construction of the second-order gravitational perturbations produced by a compact object
• 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
• High post-Newtonian order gravitational self-force analytical results for eccentric orbits around a Kerr black hole
• High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

Cited by in corpus (19)

• An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
• Self-force and radiation reaction in general relativity
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Complete waveform model for compact binaries on eccentric orbits
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
• Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
• 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
• Spin-multipole effects in binary black holes and the test-body limit
• Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription
• Redshift factor and the first law of binary black hole mechanics in numerical simulations
• Assessing the Energetics of Spinning Binary Black Hole Systems
• Gravitational radiation contributions to the two-body scattering angle
• An effective-gravity perspective on the Sun-Jupiter-comet three-body system
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Multipolar Particles in Helically Symmetric Spacetimes
• Solar system dynamics in general relativity
• On the foundations of general relativistic celestial mechanics