Geometrical Models of the Locally Anisotropic Space-Time

Abstract

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

35 pages, 5 figures, to appear in the Russian journal Hypercompl. Numb. Geom. Phys; submit/0362894 (George Bogoslovsky)

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• Berwald spacetimes and very special relativity
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• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• Finsler geometric perspective on the bulk flow in the universe
• Affine sphere spacetimes which satisfy the relativity principle
• Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment
• Generalized Finsler geometry and the anisotropic tearing of skin
• Conformal maps between pseudo-Finsler spaces
• Hyperbolic statics in space-time
• On Geometrization of Classical Fields (Model of Embedded Spaces)