Sourcefree integration method for black hole perturbations and selfforce computation: Radial fall
Abstract
Perturbations of SchwarzschildDroste black holes in the ReggeWheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C^{0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in the time domain. The forward time value in the upper node of the (t,r^{*}) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).
 Publication:

Physical Review D
 Pub Date:
 March 2011
 DOI:
 10.1103/PhysRevD.83.064029
 arXiv:
 arXiv:1008.2507
 Bibcode:
 2011PhRvD..83f4029A
 Keywords:

 04.25.Nx;
 04.30.Db;
 04.30.Nk;
 04.70.Bw;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Wave generation and sources;
 Wave propagation and interactions;
 Classical black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 Mathematical Physics
 EPrint:
 This arXiv version differs from the one to be published by Phys. Rev. D for the use of British English and other minor editorial differences