Considering Spin in Analytic Solutions to Binary Inspirals Using the Dynamical Renormalization Group Formalism

LIGO's detection of gravitational waves from coalescing binary black holes and neutron stars provided the unprecedented opportunity to study strong gravitational fields and compact binary dynamics. Furthermore, it has become vital for calculations of binaries' trajectories to have the highest possible efficiency and accuracy. When there exist many oscillations in the waveform due to binaries having lower masses, it is possible to calculate solutions to their motion via post-Newtonian expansions. The derivation of binaries' center-of-mass trajectories using the dynamical renormalization group (DRG) formalism was first introduced by Galley and Rothstein, who showed that the method had higher predictive power than and eliminates ambiguities in conventional orbit-averaged methods. While they included the radiation reaction force experienced by the binaries, we began to consider the binaries' spins as well. In this project, we derived the binaries' center-of-mass equations of motion in polar coordinates accounting for both radiation reaction and spin, generated graphical models of the trajectories, and began to derive the new DRG solution.