Covariant Renormalizable Anisotropic Theories and Off-Diagonal Einstein-Yang-Mills-Higgs Solutions

TL;DR

This paper develops a method to find exact off-diagonal solutions in covariant gravity theories with potential renormalizability, including Einstein-Yang-Mills-Higgs fields, using nonholonomic frames and spacetime decompositions.

Contribution

It introduces a decoupling approach for Einstein equations in nonholonomic frames, enabling the construction of off-diagonal solutions in covariant, potentially renormalizable gravity models.

Findings

Derived exact off-diagonal solutions with generic spacetime dependence.

Linked off-diagonal Einstein manifolds to covariant gravity theories with good ultraviolet behavior.

Extended solutions to include Einstein-Yang-Mills-Higgs fields in covariant renormalizable models.

Abstract

We use an important decoupling property of gravitational field equations in the general relativity theory and modifications, written with respect to nonholonomic frames with 2+2 spacetime decomposition. This allows us to integrate the Einstein equations (eqs) in very general forms with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un--)broken symmetry parameters. We associate families of off-diagonal Einstein manifolds to certain classes of covariant gravity theories which have a nice ultraviolet behavior and seem to be (super) renormalizable in a sense of covariant modifications of Horava-Lifshits gravity. The apparent breaking of Lorentz invariance is present in some "partner" anisotropically induced theories due to nonlinear coupling with effective parametric interactions determined by nonholonomic constraints and generic off-diagonal gravitational and matter fields configurations. Finally, we show how the constructions can be extended to include exact solutions for conjectured covariant reonormalizable models with Einstein-Yang-Mills-Higgs fields.