On Finsler spacetimes with a timelike Killing vector field

TL;DR

This paper explores Finsler spacetimes with timelike Killing vector fields, introducing a new class called stationary splitting Finsler spacetimes, and analyzes their causal structures and local properties.

Contribution

It introduces stationary splitting Finsler spacetimes and characterizes when a Finsler spacetime with a timelike Killing vector field is locally of this type.

Findings

Causal structure of stationary splitting matches that of associated static Finsler spacetimes.

Characterization of when a Finsler spacetime is locally a stationary splitting.

Introduction of a new class of Finsler spacetimes with a timelike Killing vector.

Abstract

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finslerian static spacetimes naturally associated to the stationary splitting.