math.DG

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# Title: 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 $L$ 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.
 Comments: 28 pages, AMSLaTex. v3: First part of the introduction and conclusions section expanded, some new references added; v3 matches the published version Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc) Journal reference: Class. Quantum Grav. 35 (2018) 085007 (28pp) DOI: 10.1088/1361-6382/aab0d9 Cite as: arXiv:1710.05318 [math.DG] (or arXiv:1710.05318v3 [math.DG] for this version)

## Submission history

From: Erasmo Caponio [view email]
[v1] Sun, 15 Oct 2017 11:34:39 GMT (32kb)
[v2] Mon, 23 Oct 2017 08:07:50 GMT (33kb)
[v3] Mon, 19 Mar 2018 13:31:02 GMT (35kb)