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

TL;DR

This paper introduces a new method for computing gravitational waveforms from particles falling radially by establishing jump conditions and avoiding direct source term integration, potentially applicable to generic orbits.

Contribution

The paper develops a novel approach using jump conditions to compute waveforms without direct source integration, improving efficiency and applicability.

Findings

Derived jump conditions for wavefunction and derivatives

Proposed a new waveform computation method

Potential application to generic orbits

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.