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
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
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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