Regular Article - Theoretical Physics
First post-Newtonian N-body problem in Einstein–Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals
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
Accepted: 21 January 2023
Published online: 2 February 2023
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.
© The Author(s) 2023
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