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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 $Omega(T)equiv 1$ 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 {em cone geodesic} is introduced consistently with both structures. As a non-relativistic application, the {em time-dependent} Zermelo navigation problem is posed rigorously, and its general solution is provided.
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology, we continu
The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and most commonly used speci
We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion. Our analytic definition relies on the use of the concept of a non-deg
We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds admits a metri
In this paper, we prove that lightlike geodesics of a pseudo-Finsler manifold and its focal points are preserved up to reparametrization by anisotropic conformal changes, using the Chern connection and the anisotropic calculus and the fact that geode