Finslerian Spaces Possessing Local Relativistic Symmetry
1999bgg | G. Yu. Bogoslovsky, H. F. Goenner

It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors \gamma 5 x 10^10 , indicated by the situation which has dev eloped in the physics of ultra-high energy cosmic rays (the absence of the gzk cutoOE), has a nontrivial solution. Its essence consists in the discovery of the so-called generalized Lorentz transformations which seem to correctly link the inertial reference frames at any values of c. Like the usual Lorentz transformations, the generalized ones are linear, possess group properties and lead to the Einstein law of addition of 3-velocities. However, their geometric meaning turns out to be differen t: they serv e as relativistic symmetry transformations of a flat anisotropic Finslerian event space rather than of Minkowski space. Consideration is given to two typ es of Finsler spaces which generalize locally isotropic Riemannian space-time of relativit y theory, e.g. Finsler spaces with a partially and entirely broken local 3D isotropy. The investigation advances argumen ts for the corresp onding generalization of the theory of fundamen tal interactions and for a sp eci® c searc h for physical effects due to local anisotropy of space-time.

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