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.

中文翻译：

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具有非标准分割和Randers之前指标的固定完整时空

使用相对论的费马原理，我们在满足观察者流形条件的稳态完备流形与兰德斯之前的度量（即兰德斯度量）之间建立了桥梁，而对单一形式没有任何限制。因此，我们根据与Randers之前的度量相关的元素（其测地线和相关距离）来描述此类时空的因果阶梯。作为这种相互作用的应用，我们获得了Killing浸没的共形图的描述以及Randers之前的度量和磁测地线的存在和多重性结果。