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

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

2008-06-24

arxiv.org/abs/0806.3808v2

Int.J.Theor.Phys.48:1973-1999,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1007/s10773-009-9973-5

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.

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