Toward a Gravitation Theory in Berwald--Finsler Space

Details Toward a Gravitation Theory in Berwald--Finsler Space Toward a Gravitation Theory in Berwald--Finsler Space

2007-11-13

arxiv.org/abs/0711.1934v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated. Nontrivial solutions of the gravitational field equation are presented.

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