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

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Abstract

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation on manifolds enabled with nonholonomic distributions is considered. We prove that, for certain types of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic noncommutative gravity theories 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 nonsymmetric gravity theories. It is concluded that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of some models and/or unconstrained solutions.

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Authors and Affiliations

  1. The Fields Institute for Research in Mathematical Science, 222 College Street, 2d Floor, Toronto, M5T 3J1, Canada

    Sergiu I. Vacaru

  2. Faculty of Mathematics, University “Al.I. Cuza” Iaşi, 700506, Iaşi, Romania

    Sergiu I. Vacaru

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  1. Sergiu I. Vacaru
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Correspondence to Sergiu I. Vacaru.

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Vacaru, S.I. Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics. Int J Theor Phys 48, 1973–1999 (2009). https://doi.org/10.1007/s10773-009-9973-5

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  • DOI: https://doi.org/10.1007/s10773-009-9973-5

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