Some criteria for Wind Riemannian completeness and existence of Cauchy hypersurfaces

Abstract

Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers metrics. Here, we further develop this notion and its applications to spacetimes, by introducing some characterizations and criteria for the completeness of WRS's. As an application, we consider a general class of spacetimes admitting a time function $t$ generated by the flow of a complete Killing vector field (generalized standard stationary spacetimes or, more precisely, SSTK ones) and derive simple criteria ensuring that its slices $t=$ constant are Cauchy. Moreover, a brief summary on the Finsler/Lorentz link for readers with some acquaintance in Lorentzian Geometry, plus some simple examples in Mathematical Relativity, are provided.

30 pages, 4 figures, contribution to the Proceedings of the 8th International Meeting on Lorentzian Geometry, GELOMA, Málaga, September 20-23, 2016

References in corpus (4)

• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• The cut locus and distance function from a closed subset of a Finsler manifold
• Zermelo navigation in pseudo-Finsler metrics

Cited by in corpus (1)

• Geodesics on strong Kropina manifolds