Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-08-05
Phys.Rev.D82:084036,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 5 eps figures
Scientific paper
10.1103/PhysRevD.82.084036
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 ${\mathsf M}\gg m$. Specifically, we study the gauge-invariant function $\rho(x)$, where $\rho$ is defined as the $O(m)$ part of the dimensionless ratio $(\hat\Omega_r/\hat\Omega_{\varphi})^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $x=[Gc^{-3}({\mathsf M}+m)\hat\Omega_{\varphi}]^{2/3}$ 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
Barack Leor
Damour Thibault
Sago Norichika
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