Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

TL;DR

This paper reformulates Einstein gravity using almost Kahler variables, explores nonsymmetric gravitational theories with nonholonomic distributions, and demonstrates conditions under which these models remain stable without instabilities.

Contribution

It introduces a novel reformulation of Einstein gravity in almost Kahler variables and analyzes stability conditions for nonsymmetric gravitational theories with nonholonomic constraints.

Findings

Certain nonholonomic constraints lead to stable effective Lagrangians.

Nonholonomic distributions can remove instabilities in nonsymmetric gravity models.

Instabilities are not inherent to nonsymmetric metrics, but depend on specific models.

Abstract

We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distributions is analyzed. There are considered some conditions when the fundamental geometric and physical objects are determined/ modified by nonholonomic deformations in general relativity or by contributions from Ricci flow theory and/or quantum gravity. We prove that in such NGT, for certain classes of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic NGT models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in NGT. Finally we conclude that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of certain models and/or classes of unconstrained solutions.