Gravitational selfforce on a particle in circular orbit around a Schwarzschild black hole
Abstract
We calculate the gravitational selfforce acting on a pointlike particle of mass μ, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenzgauge metric perturbation using numerical evolution in the time domain; we then compute the (finite) backreaction force from each of the multipole modes of the perturbation; finally, we apply the “modesum” method to obtain the total, physical selfforce. The temporal component of the selfforce (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitationalwave energy radiated to infinity and through the event horizon. The radial component of the selfforce (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the O(μ) correction to the specific energy and angular momentum parameters (in the Lorenz gauge), as well as the O(μ) shift in the orbital frequency (which is gauge invariant).
 Publication:

Physical Review D
 Pub Date:
 March 2007
 DOI:
 10.1103/PhysRevD.75.064021
 arXiv:
 arXiv:grqc/0701069
 Bibcode:
 2007PhRvD..75f4021B
 Keywords:

 04.25.Nx;
 04.30.Db;
 04.70.Bw;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Wave generation and sources;
 Classical black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 31 pages, 17 figures. v3 corrects typos in Eqs. (21) and (22). These typos do not propagate, and the rest of the paper remains unaffected