Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order

TL;DR

This paper derives the second post-Newtonian order gravitational-wave energy loss for inspiralling binary systems, highlighting the importance of 2PN terms for accurate gravitational-wave signal modeling.

Contribution

It provides a new, detailed derivation of 2PN corrections to gravitational radiation from binary systems, including finite mass effects, using two independent methods.

Findings

2PN terms significantly affect the phase evolution of gravitational waves.

Finite mass contributions are crucial for accurate waveform templates.

The results improve the precision of gravitational-wave data analysis.

Abstract

The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order $O[(Gm/rc^2)^2]$ beyond the quadrupole approximation. The result has been derived by two independent calculations of the (source) multipole moments. The 2PN terms, and in particular the finite mass contribution therein (which cannot be obtained in perturbation calculations of black hole spacetimes), are shown to make a significant contribution to the accumulated phase of theoretical templates to be used in matched filtering of the data from future gravitational-wave detectors.