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Using the relativistic Fermat's principle, we establish a bridge betweenstationary-complete manifolds which satisfy the observer-manifold condition andpre-Randers metrics, namely, Randers metrics without any restriction on theone-form. As a consequence, we give a description of the causal ladder of suchspacetimes in terms of the elements associated with the pre-Randers metric: itsgeodesics and the associated distance. We obtain, as applications of thisinterplay, the description of conformal maps of Killing submersions, andexistence and multiplicity results for geodesics of pre-Randers metrics andmagnetic geodesics.

Stationary-Complete Spacetimes with non-standard splittings and pre-Randers metrics