abstract: In general relativity the velocity space is described by the hyperboloid \(\mathbb{H}^3\). By considering alternative velocity spaces one is lead to Lorentz-Finsler geometry. I present some recent proposals for modifications of the velocity space of general relativity, in particular I shall describe the nice properties of a theory based on affine sphere indicatrices.
Talk partly based on the paper "Affine Sphere Relativity" Communications in Mathematical Physics 350 (2017) 749–801