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

TL;DR

This paper explores the relationship between certain stationary spacetimes and pre-Randers metrics, providing new insights into their causal structure, geodesics, and conformal maps, with applications to magnetic geodesics.

Contribution

It establishes a novel connection between stationary-complete spacetimes satisfying the observer-manifold condition and pre-Randers metrics, expanding the understanding of their geometric and causal properties.

Findings

Describes the causal ladder of such spacetimes in terms of pre-Randers metric elements.

Provides results on conformal maps of Killing submersions.

Proves existence and multiplicity of geodesics and magnetic geodesics.

Abstract

Using the relativistic Fermat's principle, we establish a bridge between stationary-complete manifolds which satisfy the observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on the one-form. As a consequence, we give a description of the causal ladder of such spacetimes in terms of the elements associated with the pre-Randers metric: its geodesics and the associated distance. We obtain, as applications of this interplay, the description of conformal maps of Killing submersions, and existence and multiplicity results for geodesics of pre-Randers metrics and magnetic geodesics.