Charged spin fluid in the Einstein-Cartan theory

We propose a variational principle describing a charged spin fluid in the Einstein-Cartan theory. We show that this fluid can be described by the current vector Vᵢ which has a potential decomposition and generalizes the results given by Taub. We also derive Maxwell's equations in the presence of spin and torsion. The Eulerian description of the fluid is given by an action integral whose Lagrangian is the pressure plus the free Lagrangians of the gravitational and electromagnetic fields. Finally, we analyze the circulation and Bernoulli theorems using the current vector Vᵢ.