Accurate and efficient GW phasing for spinning compact binaries

An approach is developed to perform gravitational wave (GW) phasing for spinning compact binaries spiraling along quasi-circular orbits.  In our approach, temporally evolving GW polarization states are specified by nine independent parameters, compared to eleven in the traditional approach. This is attributable to the use of orbital angular momentum to describe binary orbits and an invariant frame associated with the initial direction of total angular momentum to freely specify the two spins. It turns out that such a reduction in the number of  independent parameters is impossible to achieve in the traditional approach that freely specify the two spin vectors in an orbital triad based on the Newtonian orbital angular momentum. A number of undesirable consequences of the traditional approach are listed including the existence of unphysical third post-Newtonian order terms in the GW phase evolution. Subtleties involved while incorporating orbital eccentricity are also detailed.