Generalized Finsler Geometry in Einstein, String and Metric--Affine Gravity

Sergiu I. Vacaru

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arXiv · hep-th/0310132

Generalized Finsler Geometry in Einstein, String and Metric--Affine Gravity

Sergiu I. Vacaru

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Abstract

We develop the method of anholonomic frames with associated nonlinear connection (in brief, N--connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler--Lagrange--Cartan--Hamilton geometry) can be modeled in the metric--affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively induced in the Einstein, teleparallel, Riemann--Cartan and metric--affine gravity. We argue that every generic off--diagonal metric (which can not be diagonalized by coordinate transforms) is related to specific N--connection configurations. We elaborate the concept of generalized Finsler--affine geometry for spaces provided with arbitrary N--connection, metric and linear connection structures and characterized by gravitational field strengths, i. e. by nontrivial N--connection curvature, Riemannian curvature, torsion and nonmetricity. We apply a irreducible decomposition techniques (in our case with additional N--connection splitting) and study the dynamics of metric--affine gravity fields generating Finsler like configurations. The classification of basic eleven classes of metric--affine spaces with generic local anisotropy is presented.

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Sergiu I. Vacaru. 2003-10-14. Generalized Finsler Geometry in Einstein, String and Metric--Affine Gravity. https://arxiv.org/abs/hep-th/0310132

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