Gravitational radiation by point particle eccentric binary systems in the linearised characteristic formulation of general relativity

TL;DR

This paper analyzes gravitational wave emission from eccentric binary systems of unequal masses using the linearized characteristic formulation of general relativity, extending previous circular orbit models and confirming classical results.

Contribution

It generalizes the characteristic formulation to eccentric, unequal-mass binaries and extends boundary conditions beyond circular orbits, providing a new tool for gravitational wave extraction.

Findings

Power loss matches Peters and Mathews 1963 results

Boundary conditions applicable to eccentric orbits

Framework for gravitational wave extraction in inspiralling binaries

Abstract

We study a binary system composed of point particles of unequal masses in eccentric orbits in the linear regime of the characteristic formulation of general relativity, generalising a previous study found in the literature in which a system of equal masses in circular orbits is considered. We also show that the boundary conditions on the time-like world tubes generated by the orbits of the particles can be extended beyond circular orbits. Concerning the power lost by the emission of gravitational waves, it is directly obtained from the Bondi's News function. It is worth stressing that our results are completely consistent, because we obtain the same result for the power derived by Peters and Mathews, in a different approach, in their seminal paper of 1963. In addition, the present study constitutes a powerful tool to construct extraction schemes in the characteristic formalism to obtain the gravitational radiation produced by binary systems during the inspiralling phase.