Binary Inspiral Gravitational Waves from a Post-Newtonian Expansion
The post-Newtonian (PN) expansion of general relativity provides the framework for calculating the waveforms of gravitational radiation for systems that are not "too" relativistic. One of the major results of the work in PN theory is waveforms for the binary inspiral problem. These "chirp" waveforms are demonstrated here for non-spinning point masses in a circular orbit. The phase and amplitudes in the expansion can be expanded to various orders, the two masses of the bodies can be varied, and the inclination of the system relative to the line of sight and the coalescence phase can also be varied. The two waveforms plotted are the two polarizations ("plus" and "cross") of the gravitational waveform.
The expressions in this notebook come from L. Blanchet, B. R. Iyer, C. M. Will, and A. G. Wiseman, "Gravitational Waveforms from Inspiralling Compact Binaries to Second-Post-Newtonian Order."