International Journal of Theoretical Physics

, Volume 49, Issue 4, pp 884–913 | Cite as

On General Solutions for Field Equations in Einstein and Higher Dimension Gravity



We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseudo) Riemannian manifolds an alternative (to the Levi-Civita connection) metric compatible linear connection which is also completely defined by the same metric structure. Such a canonically distinguished connection is with nontrivial torsion which is induced by some nonholonomy frame coefficients and generic off-diagonal terms of metrics. It is possible to define certain classes of adapted frames of reference when the Einstein equations for such an alternative connection transform into a system of partial differential equations which can be integrated in very general forms. Imposing nonholonomic constraints on generalized metrics and connections and adapted frames (selecting Levi-Civita configurations), we generate exact solutions in Einstein gravity and extra dimension generalizations.


Einstein spaces and higher dimension gravity Anholonomic frames Exact solutions Nonholonomic manifolds 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Science DepartmentUniversity “Al. I. Cuza” IaşiIaşiRomania

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