On Finsler spacetimes with a timelike Killing vector field

Understand

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.