Normal geodesics connecting two non-necessarily spacelike submanifolds in a stationary spacetime

TL;DR

This paper proves the existence of normal geodesics connecting two submanifolds in a stationary spacetime, including non-spacelike cases, using variational and geometric methods involving causal structures and Finsler metrics.

Contribution

It extends previous results by establishing existence for non-spacelike submanifolds in stationary spacetimes through a novel combination of variational and geometric techniques.

Findings

Existence theorem for normal geodesics in stationary spacetimes.

Handles non-spacelike submanifolds, broadening applicability.

Uses Finsler metrics and causal structure in the proof.

Abstract

In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime. The proof is based on both variational and geometric arguments involving the causal structure of the spacetime, the completeness of suitable Finsler metrics associated to it and some basic properties of a submersion. By this interaction, unlike previous results on the topic, also non--spacelike submanifolds can be handled.