Point Particle Binary System with Components of Different Masses in the Linear Regime of the Characteristic Formulation of General Relativity

TL;DR

This paper analyzes gravitational wave emission from a binary system of two point particles with different masses within the linear characteristic formulation of general relativity, confirming known results and exploring multipole contributions.

Contribution

It generalizes previous studies by including unequal masses and decomposing metric variables in spin-weighted spherical harmonics within the characteristic formulation.

Findings

Power emitted matches Peters and Mathews' classical results.

Boundary conditions at world tubes are explicitly explored.

Multiple multipole contributions to gravitational radiation are analyzed.

Abstract

A study of binary systems composed of two point particles with different masses in the linear regime of the characteristic formulation of general relativity in a Minkowski background is provided. The present paper generalizes a previous study find in the literature. The boundary conditions at the world tubes generated by the particle's orbits are explored, when the metric variables are decomposed in spin-weighted spherical harmonics. The power lost by the emission of gravitational waves is computed using the News Bondi's functions. The power found is nothing but the well-known result for the power obtained by Peters and Mathews in a different approach. This agreement shows the consistency of the approach considered here. The contribution to the gravitational radiation of several multipole terms is also shown.