On the various aspects of electromagnetic potentials in spacetimes with   symmetries
  We revise and generalize the properties of the electric and the magnetic scalar potentials in spacetimes admitting a Killing vector field: Their constancy on the Killing horizons, uniqueness of solution for the electromagnetic test fields and the relation between the Bianchi identity and Maxwell's equations. In each of these examples, collinearity of currents with the Killing vector field is shown to be the crucial property. 
Ivica Smoli\'c
gr-qc hep-th