Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries

TL;DR

This paper derives a fully reduced Hamiltonian for next-to-leading order spin-squared dynamics in general compact binaries, applicable to black holes and neutron stars, incorporating spin-induced quadrupolar effects within the post-Newtonian framework.

Contribution

It provides the first fully reduced Hamiltonian formulation for spin-squared interactions at this order, facilitating canonical equations of motion for complex binary systems.

Findings

Hamiltonian applicable to all compact binaries with spin-induced quadrupolar effects

Equations of motion expressed in canonical Poisson brackets

Comparison with EFT potential shows consistency and differences

Abstract

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.