ADM canonical formulation with spin and application to post-Newtonian approximations

TL;DR

This paper extends the ADM canonical formalism to include spin effects in binary black holes, enabling higher-order post-Newtonian calculations crucial for improving gravitational wave templates.

Contribution

It develops a method to incorporate spin into the ADM formalism using Poincare invariance, achieving high-order accuracy in both spin and PN expansion.

Findings

Extended ADM formalism to spinning black holes.

Achieved high-order accuracy in spin and PN expansion.

Facilitated more precise gravitational wave templates.

Abstract

Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be used in future gravitational wave astronomy. We focus on the extension of the ADM canonical formalism to spinning binary black holes. Using the global Poincare invariance of asymptotically flat spacetimes as the most important guiding consistency condition, this extension can be constructed order by order in the PN approximation. We were able to reach a high order both in the spin power and the PN counting.