Self-force and radial fall: new integration method for the Zerilli wave equation

Abstract

We establish the jump conditions for the wavefunction and its derivatives through the formal solutions of the wave equation. These conditions respond to the requirement of continuity of the perturbations at the position of the particle and they are given for any mode at first order. Using these jump conditions, we then propose a new method for computing the radiated waveform without direct integration of the source term. We consider this approach potentially applicable to generic orbits.