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

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.