Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
arXiv:0806.3808 · doi:10.1007/s10773-009-9973-5
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
References in corpus (10)
- Testing modified gravity with globular cluster velocity dispersions
- Finsler and Lagrange Geometries in Einstein and String Gravity
- Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
- Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
- Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
- Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
- Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
- Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
- Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
- Problems and hopes in nonsymmetric gravity