Kinetic dynamics of neutral spin particles in a spacetime with torsion

TL;DR

This paper develops a kinetic model for collisionless neutral spin particles in spacetimes with torsion, generalizing the Vlasov equation to include spin effects and ensuring particle number conservation through a two-species approach.

Contribution

It introduces a novel kinetic equation for spinful particles in torsionful spacetimes and addresses particle number conservation by considering two particle species.

Findings

Derived a generalized Vlasov equation for spin particles with torsion.

Established a method to conserve total particle number using two species.

Connected the kinetic model with Einstein-Cartan theory via the Bianchi identity.

Abstract

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 $\overline{f}$ of the new particles is derived by requiring that the sum of total numbers of particles of the two species should be conserved.