%0 Journal Article
%T On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
%A Sergiu I. Vacaru
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s10773-010-0271-z
%X 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.
%U http://arxiv.org/abs/0909.3949v4