Kaluza's kinetic theory description of the classical Hall effect in a single component dilute gas within the Chapman-Enskog approximation

Kinetic theory is used to establish the explicit form of the particle flux associated to the Hall effect for the case of a dilute single component charged gas, using the Chapman-Enskog method and the BGK approximation for the collision Kernel. It is shown that when the system evolves towards mechanical equilibrium, the standard treatment using the concept of external force fails to describe the Hall effect. It is also shown that the use of a five-dimensional curved space-time in the description of the dynamics of the charged particle in the kinetic treatment (Kaluza's theory) formally solves the problem. The implications of this result are briefly discussed.