Lorenz gauge gravitational selfforce calculations of eccentric binaries using a frequency domain procedure
Abstract
We present an algorithm for calculating the metric perturbations and gravitational selfforce for extrememassratio inspirals (EMRIs) with eccentric orbits. The massive black hole is taken to be Schwarzschild, and metric perturbations are computed in Lorenz gauge. The perturbation equations are solved as coupled systems of ordinary differential equations in the frequency domain. Accurate local behavior of the metric is attained through use of the method of extended homogeneous solutions, and modesum regularization is used to find the selfforce. We focus on calculating the selfforce with sufficient accuracy to ensure its error contributions to the phase in a longterm orbital evolution will be δ Φ ≲1 0^{2} rad . This requires the orbitaveraged force to have fractional errors ≲1 0^{8} and the oscillatory part of the selfforce to have errors ≲1 0^{3} (a level frequently easily exceeded). Our code meets this error requirement in the oscillatory part, extending the reach to EMRIs with eccentricities of e ≲0.8 , if augmented by use of fluxes for the orbitaveraged force, or to eccentricities of e ≲0.5 when used as a standalone code. Further, we demonstrate accurate calculations up to orbital separations of a ≃100 M , beyond that required for EMRI models and useful for comparison with postNewtonian theory. Our principal developments include (1) use of fully constrained field equations, (2) discovery of analytic solutions for evenparity static modes, (3) finding a preconditioning technique for outer homogeneous solutions, (4) adaptive use of quad precision, (5) jump conditions to handle nearstatic modes, and (6) a hybrid scheme for high eccentricities.
 Publication:

Physical Review D
 Pub Date:
 November 2014
 DOI:
 10.1103/PhysRevD.90.104031
 arXiv:
 arXiv:1409.4419
 Bibcode:
 2014PhRvD..90j4031O
 Keywords:

 04.25.dg;
 04.30.w;
 04.25.Nx;
 04.30.Db;
 Numerical studies of black holes and blackhole binaries;
 Gravitational waves: theory;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Wave generation and sources;
 General Relativity and Quantum Cosmology
 EPrint:
 Updated to more closely reflect published version