Publication: On the definition and examples of cones and Finsler spacetimes
Authors
Javaloyes, Miguel Ángel ; Sánchez, Miguel
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Publisher
Springer
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DOI
https://doi.org/10.1007/s13398-019-00736-y
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info:eu-repo/semantics/article
Description
© 2019 Authors
This document is the published version of a published work that appeared in final form in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
To access the final edited and published work see: https://doi.org/10.1007/s13398-019-00736-y
Abstract
A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (, T , F), where (resp. T ) is a 1-form (resp. vector field) with (T ) ≡ 1 and F, a Finsler metric on ker(), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non- relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.
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Citation
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. Volumen 114, artículo 30, 2020.
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1-ene-2999
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