On the definition and examples of cones and Finsler spacetimes

Understand

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.