Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

P. Ritter (1, 2) , S. Aoudia (3) , Alessandro D. A. M. Spallicci (2) , Stéphane Cordier (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LPC2E - Laboratoire de Physique et Chimie de l'Environnement et de l'Espace
3 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

Keywords: Modelling of wave equation; General relativity; Equations of motion; Two-body problem; Gravitational waves; Black holes

Domains: General Relativity and Quantum Cosmology [gr-qc]; Mathematical Physics [math-ph]; Astrophysics [astro-ph]

P. Ritter, S. Aoudia, Alessandro D. A. M. Spallicci, Stéphane Cordier. Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs. International Journal of Geometric Methods in Modern Physics, 2016, 13 (02), pp.1650021. ⟨10.1142/S0219887816500213⟩. ⟨insu-01352533⟩