First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals

TL;DR

This paper derives the first post-Newtonian equations of motion for an N-body system in Einstein-Cartan theory, incorporating quantum spin effects via Weyssenhoff fluid, and analyzes binary systems' dynamics and spin precession.

Contribution

It introduces a Lagrangian formulation and first integrals for the post-Newtonian dynamics of spinning bodies in Einstein-Cartan theory, extending previous models to include quantum spin effects.

Findings

Derived equations of motion for N-body systems with spin in Einstein-Cartan theory.

Established Lagrangian and first integrals for binary systems.

Analyzed spin precession within the post-Newtonian framework.

Abstract

The rotational dynamics of an $N$-body system at the first post-Newtonian order in Einstein-Cartan theory is derived. This result is achieved by performing the point-particle limit of the equations of motion of the Weyssenhoff fluid, which models the quantum spin effects residing inside the bodies. For the special case of binary systems, we determine the Lagrangian function and the resulting first integrals underlying the translational dynamics and the spin precession.