Finslerian spaces possessing local relativistic symmetry

Details Finslerian spaces possessing local relativistic symmetry Finslerian spaces possessing local relativistic symmetry

1999-04-30

arxiv.org/abs/gr-qc/9904081v1

Gen.Rel.Grav. 31 (1999) 1565-1603

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages, 1 table, 4 figures, latex

Scientific paper

It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $\gamma >5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence of the GZK cutoff), 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 $\gamma .$ 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 different: they serve as relativistic symmetry transformations of a flat anisotropic Finslerian event space rather than of Minkowski space. Consideration is given to two types of Finsler spaces which generalize locally isotropic Riemannian space-time of relativity theory, e. g. Finsler spaces with a partially and entirely broken local 3D isotropy. The investigation advances arguments for the corresponding generalization of the theory of fundamental interactions and for a specific search for physical effects due to local anisotropy of space-time.

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