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

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.

latex2e, 11pt, 41 pages, new and up-dated references and discussion

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Cited by in corpus (11)

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• On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
• Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• Nonassociative geometry of nonholonomic phase spaces with star R-flux string deformations and (non) symmetric metrics
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Branes and Quantization for an A-Model Complexification of Einstein Gravity in Almost Kahler Variables
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity
• Signatures of Noncommutative Geometry in Muon Decay for Nonsymmetric Gravity