Integrability and action-angle-based solution of the post-Newtonian BBH system (lecture notes)

TL;DR

This paper provides lecture notes that explain how to solve the dynamics of spinning, eccentric binary black holes at 1.5PN order using integrability and action-angle variables, making advanced methods accessible.

Contribution

It offers a comprehensive introduction to the symplectic geometric approach necessary for understanding closed-form solutions of binary black hole systems at 1.5PN.

Findings

Closed-form solutions for spinning, eccentric BBH dynamics at 1.5PN

Two equivalent methods: Hamilton integration and action-angle variables

Prerequisite knowledge of symplectic geometry provided

Abstract

These lecture notes are based on Refs. arXiv:2110.15351, arXiv:2012.06586, and arXiv:1908.02927, which aim to give closed-form solutions to the spinning, eccentric binary black hole dynamics at 1.5PN via two different equivalent ways: (1) the standard way of integrating Hamilton's equations and (2) using action-angle variables. The above papers assume a certain level of familiarity with the symplectic geometric approach to classical mechanics, the non-fulfillment of which on the reader's part may make the papers appear esoteric. The purpose of these lecture notes is to give the reader this prerequisite knowledge which the above papers assume on the reader's part.