Minimal coupling of electromagnetic fields in Riemann–Cartan space‐times for perfect fluids with spin density

Abstract

The electromagnetic field is minimally coupled to gravity in a Riemann–Cartan space‐time containing a charged magnetized spinning fluid. It is required that the overall Lagrangian of the gravitational field, spinning matter, and the electromagnetic field be invariant under a gauge transformation of the vector potential. The theory preserves both charge conservation and particle number conservation. The electromagnetic field, via the vector potential, now interacts directly with the spin energy momentum. The spin transport equation, in addition to the usual Fermi–Walker transport term, contains a contribution due to the torque of the electromagnetic field acting on a magnetic dipole. In the absence of electromagnetism, the field equations reduce to those of the usual self‐consistent Lagrangian formalism for a perfect fluid with spin density.