期刊
出版社
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13398-019-00736-y
关键词
Finsler spacetime; Lorentz-Finsler metrics and norms; Cone structure; Static and stationary spacetimes; Zermelo navigation problem; Generalized Fermat principle
资金
- MINECO/FEDER project, Spain [MTM2015-65430-P]
- Fundacion Seneca, Spain [19901/GERM/15]
- Spanish MINECO/ERDF project [MTM2016-78807-C2-1-P]
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 (omega,T,F), where omega (resp. T) is a 1-form (resp. vector field) with omega(T)equivalent to 1 and F, a Finsler metric on ker(omega), 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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