KINETIC DYNAMICS OF NEUTRAL SPIN PARTICLES IN A SPACETIME WITH TORSION

Journal article, 2025

A kinetic model for the dynamics of collisionless spin neutral particles in a spacetime with torsion is proposed. The fundamental matter field is the kinetic density f(x, u, s) of particles with four-velocity u and four-spin s. The stress-energy tensor and the spin current of the particles distribution are defined as suitable integral moments of f in the (u, s) variables. By requiring compatibility with the contracted Bianchi identity in Einstein–Cartan theory, we derive a transport equation on the kinetic density f that generalizes the well-known Vlasov equation for spinless particles. The total number of particles in the new model is not conserved. To restore this important property, we assume the existence in spacetime of a second species of particles with the same mass and spin magnitude. The Vlasov equation on the kinetic density f̄ of the new particles is derived by requiring that the sum of the total numbers of particles of the two species should be conserved.