Nonholomic Distributions and Gauge Models of Einstein Gravity

TL;DR

This paper explores how Einstein gravity can be reformulated using nonholonomic distributions and gauge models, revealing hidden geometric structures and potential applications in classical and quantum gravity.

Contribution

It introduces a new geometric framework for Einstein gravity based on nonholonomic deformations and gauge models, uncovering hidden structures and quantum aspects.

Findings

Reformulation of Einstein equations in nonholonomic variables.

Identification of gauge models equivalent to Einstein gravity.

Potential applications in classical and quantum gravity.

Abstract

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.