Gravitational selfforce on a particle in eccentric orbit around a Schwarzschild black hole
Abstract
We present a numerical code for calculating the local gravitational selfforce acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenzgauge metric perturbation equations (sourced by the deltafunction particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical selfforce along the orbit is then obtained via modesum regularization. The total selfforce contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a timedomain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wavezone numerical solutions. The conservative piece of the selfforce does not affect the timeaveraged rate of energy and angularmomentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strongfield orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative selfforce [Phys. Rev. Lett. 102, 191101 (2009)PRLTAO0031900710.1103/PhysRevLett.102.191101]. Here we provide full details of this analysis, and discuss future applications.
 Publication:

Physical Review D
 Pub Date:
 April 2010
 DOI:
 10.1103/PhysRevD.81.084021
 arXiv:
 arXiv:1002.2386
 Bibcode:
 2010PhRvD..81h4021B
 Keywords:

 04.25.Nx;
 04.30.Db;
 04.40.b;
 04.70.Bw;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Wave generation and sources;
 Selfgravitating systems;
 continuous media and classical fields in curved spacetime;
 Classical black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 42 pages. v3 corrects typos in Eqs. (3.11), (3.12), (4.2), (E25) and (E26)