Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
- School of Mathematics, University of Southampton, Southampton SO17 1BJ (United Kingdom)
- Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette (France)
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the O(m) conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass m moving around a Schwarzschild black hole of mass M>>m. Specifically, we study the gauge-invariant function {rho}(x), where {rho} is defined as the O(m) part of the dimensionless ratio ({Omega}-circumflex{sub r}/{Omega}-circumflex{sub {phi}}){sup 2} between the squares of the radial and azimuthal frequencies of the orbit, and where x=[Gc{sup -3}(M+m){Omega}-circumflex{sub {phi}}]{sup 2/3} is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function {rho}(x) in the interval 0<x{<=}1/6 determines, for the first time, the strong-field behavior of a combination of two of the basic functions entering the effective one-body (EOB) description of the conservative dynamics of binary systems. We show that our results agree well in the weak-field regime (small x) with the 3rd post-Newtonian (PN) expansion of the EOB results, and that this agreement is improved when taking into account the analytic values of some of the logarithmic-running terms occurring at higher PN orders. Furthermore, we demonstrate that GSF data give access to higher-order PN terms of {rho}(x) and can be used to set useful new constraints on the values of yet-undetermined EOB parameters. Most significantly, we observe that an excellent global representation of {rho}(x) can be obtained using a simple '2-point' Pade approximant which combines 3PN knowledge at x=0 with GSF information at a single strong-field point (say, x=1/6).
- OSTI ID:
- 21432399
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 8; Other Information: DOI: 10.1103/PhysRevD.82.084036; (c) 2010 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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