Nonholomic Distributions and Gauge Models of Einstein Gravity

Details Nonholomic Distributions and Gauge Models of Einstein Gravity Nonholomic Distributions and Gauge Models of Einstein Gravity

2009-02-05

arxiv.org/abs/0902.0911v4

Int.J.Geom.Meth.Mod.Phys.7:215-246,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v4,latex2e, 39 pages, accepted for IJGMMP 7 (2010)

Scientific paper

For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi-Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric tensor. Reformulation of the Einstein equations in nonholonomic variables (tetrads and new connections, for instance, with constant coefficient curvatures and/or Yang-Mills like potentials) reveals hidden geometric and rich quantum structures. It is shown how the Einstein gravity theory can be re-defined equivalently as certain gauge models on nonholonomic affine and/or de Sitter frame bundles. We speculate on possible applications of the geometry of nonholonomic distributions with associated nonlinear connections in classical and quantum gravity.

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