Abstract

Accurate gravitational waveforms are necessary for LIGO and LISA sources, and especially for the prospect of multi-band gravitational wave observations. Computing these waveforms accurately is expensive because of the complicated precession dynamics over a very large number of orbits. The most complicated scenario is an eccentric binary where both spins and the orbital plane are precessing. Current state-of-the-art waveform models rely on analytical approximations like orbit averaging and a small-eccentricity expansion. I will present work towards avoiding these approximations by exploiting integrability of the Hamiltonian dynamics of eccentric, spinning black hole binaries. Integrability lets us construct action-angle variables, which make the evolution very simple for arbitrarily long times. I will present how to construct the action integrals (involving lifting via a momentum map) and angle variables at 1.5PN. And while post-Newtonian corrections break integrability, we can recover it in a perturbative sense. I will also present explicit (perturbative) constants of motion at 2PN order, and the method that we used to find them. (Based on 2012.06586 and 2110.15351)