On Finsler spacetimes with a timelike Killing vector field
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 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.
Keywords
Cite
@article{arxiv.1710.05318,
title = {On Finsler spacetimes with a timelike Killing vector field},
author = {Erasmo Caponio and Giuseppe Stancarone},
journal= {arXiv preprint arXiv:1710.05318},
year = {2018}
}
Comments
28 pages, AMSLaTex. v3: First part of the introduction and conclusions section expanded, some new references added; v3 matches the published version