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

Emmanuele Battista; Vittorio De Falco

doi:10.1140/epjc/s10052-022-10746-7

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 782
https://doi.org/10.1140/epjc/s10052-022-10746-7

Regular Article - Theoretical Physics

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

Emmanuele Battista¹^a and Vittorio De Falco²^,3

¹ Department of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
² Scuola Superiore Meridionale, Largo San Marcellino 10, 80138, Naples, Italy
³ Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Naples, Italy

^a emmanuele.battista@univie.ac.at, emmanuelebattista@gmail.com

Received: 17 July 2022
Accepted: 20 August 2022
Published online: 3 September 2022

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.

© The Author(s) 2022

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