Fast spectral source integration in black hole perturbation calculations
Abstract
This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational selfforce calculations involving extreme mass ratios and generic orbits. Called spectral source integration (SSI), this method should see widespread future use in problems that entail (i) a pointparticle description of the small compact object, (ii) frequency domain decomposition, and (iii) the use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory fluxbalance calculations and in local gravitational selfforce calculations. Recent selfforce calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as e ≃0.7 . We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of 3 improvement in the overall speed. The primary initial application of SSI—for us its the raison d'être—is in an arbitrary precision mathematica code that computes perturbations of eccentric orbits in the ReggeWheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These highaccuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr and will be the subject of a later publication. SSI borrows concepts from discretetime signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in a solution of the geodesic orbital motion.
 Publication:

Physical Review D
 Pub Date:
 August 2015
 DOI:
 10.1103/PhysRevD.92.044048
 arXiv:
 arXiv:1506.04742
 Bibcode:
 2015PhRvD..92d4048H
 Keywords:

 04.25.dg;
 04.25.Nx;
 04.30.w;
 04.30.Db;
 Numerical studies of black holes and blackhole binaries;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Gravitational waves: theory;
 Wave generation and sources;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 7 figures