Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries

TL;DR

This paper derives a highly precise Hamiltonian model for the spin interactions in binary systems of compact objects, crucial for accurate gravitational wave predictions.

Contribution

It provides the next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian, advancing the modeling of spinning binary systems in general relativity.

Findings

Hamiltonian matches Poincare algebra constraints

Interaction strength comparable to 4PN effects for rapid spins

Center-of-mass vector determined by ansatz

Abstract

We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.