First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: equations of motion

TL;DR

This paper derives the first post-Newtonian equations of motion for an N-body system in Einstein-Cartan gravity using Weyssenhoff fluid as a spin model, exploring the effacing principle and angular momentum analogies.

Contribution

It presents the first derivation of 1PN equations of motion in Einstein-Cartan theory with a spin fluid model, extending gravitational dynamics understanding.

Findings

Equations suggest the validity of the effacing principle at 1PN in Einstein-Cartan.

Analogies with general relativity's angular momentum dynamics are discussed.

Point-particle limit of spin fluids is successfully performed.

Abstract

We derive the equations of motion for an $N$-body system in the Einstein-Cartan gravity theory at the first post-Newtonian order by exploiting the Weyssenhoff fluid as the spin model. Our approach consists in performing the point-particle limit of the continuous description of the gravitational source. The final equations provide a hint for the validity of the effacing principle at 1PN level in Einstein-Cartan model. The analogies with the general relativistic dynamics involving the macroscopic angular momentum are also discussed.