Eccentric catastrophes & what to do with them

Analytic modeling of gravitational waves (GWs) from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the Fourier integral in non-monotonic, resulting in a breakdown of the standard stationary phase approximation (SPA). In this work, we study this breakdown within the context of catastrophe theory. We find that the SPA holds in the context of eccentric Keplerian orbits when the Fourier frequency satisfies fmin

Automated summary

This study examines the breakdown of non-stationary phase approximation in eccentric Keplerian orbits and finds that the approximation holds under specific conditions of Fourier frequency.