Causal ladder of Finsler spacetimes with a cone Killing vector field

TL;DR

This paper explores the causal properties of Finsler spacetimes with cone structures and cone Killing vector fields, especially focusing on Finsler-Kropina metrics, deepening the understanding of their geometric and causality relations.

Contribution

It introduces the concept of cone Killing vector fields in cone structures and relates causality in Finsler spacetimes to metric properties of wind Finslerian structures, especially Finsler-Kropina metrics.

Findings

Causality properties are characterized via metric-type properties of wind Finslerian structures.

The study emphasizes Finsler-Kropina metrics with strongly convex indicatrices.

A detailed analysis of cone structures associated with Finsler-Kropina metrics is provided.

Abstract

The correspondence between wind Riemannian structures and spacetimes endowed with a Killing vector field is deepened by considering a cone structure endowed with a vector field that preserve the structure (termed "cone Killing vector field") and a wind Finslerian structure. Causality properties of the former are characterized by using metric-type properties of the latter. A particular attention is posed to the case of a cone structure associated with a Finsler-Kropina type metric, i.e. a field of compact and strongly convex indicatrices that enclose the zero vector in the closure of its bounded interior at each tangent space of the manifold.