**Authors**: Leor Barack, Norichika Sago

**Date**: 17 Jan 2011

**Abstract**: We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass $\mu$ is much smaller than the black hole mass $M$, and explore post-geodesic corrections of $O(\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $O(\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit "red shift" invariant. We compute the $O(\mu/M)$ conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly-gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

1101.3331
(/preprints)

2011-01-20, 09:23
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*