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

TL;DR

This paper extends a time-domain integration method for black hole perturbations to generic EMRI orbits, enabling accurate waveform and flux calculations crucial for gravitational wave astronomy.

Contribution

It applies a finite difference scheme with jump conditions to second order for geodesic EMRI orbits, improving waveform modeling without direct source integration.

Findings

Accurate wave-forms for various EMRI orbits obtained

Comparison shows consistency with other methods

Method effectively handles orbit complexities like zoom-whirl

Abstract

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).