Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry

By S. Detweiler. 2008

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A small mass {mu} in orbit about a much more massive black hole m moves along a world line that deviates from a geodesic of the black hole geometry by O({mu}/m). This deviation is said to be caused by the gravitational self-force of the metric perturbation h{sub ab} from {mu}. For circular orbits about a nonrotating black hole we numerically calculate the O({mu}/m) effects upon the orbital frequency and upon the rate of passage of proper time on the world line. These two effects are independent of the choice of gauge for h{sub ab} and are observable in principle. For distant orbits, our numerical results agree with a post-Newtonian analysis including terms of order (v/c){sup 6}.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/9538547cbc2549a5e96611d47938ace6a16402f3

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In Astronomy and Astrophysics

Citations in the corpus

The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “ns (13PN). These have not yet been reproduced in the PN framework. 59 What is remarkable about these manipulations is the following. While the comparison for certain gauge invariant observables, e.g. [413], can be safely made in the extreme-mass-ratio regime, qm ˝1, 59 The second-order self-force is”
The Motion of Point Particles in Curved Spacetime (2003, methodology): “The mode-sum method was also used to compute unambiguous physical effects associated with the gravitational self-force [50, 157, 11], and these results were involved in detailed comparisons with post-Newtonian theory [50, 29, 28, 44, 11].”
Black hole perturbation theory and gravitational self-force (2021, background): “However, for orbits in Schwarzschild spacetime and for equatorial orbits in Kerr, snapshot frequencydomain calculations of the complete h((1)) μν and f μ (1) are now routine, whether in the Lorenz gauge, Regge-Wheeler-Zerilli gauge, or no-string radiation gauge [12, 48, 13, 1, 180, 56, 2, 136, 206, ”
Gravitational self-force in a Schwarzschild background and the effective one-body formalism (2009, background): “ear-zone metric of a gravitating system [44] give rise to a (Renormalization-Group-type) logarithmic 38 running of the expansion coeﬃcients of various functions: the “redshift” function ut(y) of Ref. [27] (for which we computed the leading logarithmic term, Eq.(7.14)), and, arguably, the EOBfunction”