GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

摘要

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still re_main compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural met_rical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more re_cent developments such as those in String theory, whereby Lorentz invariance is partially broken.