Relativistic Finsler geometry

Abstract

We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By dropping the quadratic restriction on the measurement of an infinitesimal distance, the geometry is generalized to a Finsler structure. Apart from curvature a new property of the manifold complicates the geometrodynamics, the color. The color brings forth an intrinsic local anisotropy and many quantities depend on position and to a "supporting" direction. We discuss this direction dependence and some physical interpretations. Also, we highlight that in Finsler geometry the parallel displacement isn't necessarily always along the "supporting" direction. The latter is a fundamental congruence of the manifold and induces a natural 1+3 decomposition. Its internal deformation is given through the evolution of the irreducible components of vorticity, shear and expansion.

references added, Contribution to the proceedings of "Modern Mathematical Methods in Science and Technology 2012 (M3ST2012)", Kalamata, Greece, August, 2012

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Cited by in corpus (5)

• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Anisotropic strange star in Finsler geometry
• Intrinsic and Extrinsic curvatures in Finsler-esque spaces
• A Novel Foamy Origin for Singlet Fermion Masses