Nonlinear Connections and Exact Solutions in Einstein and Extra Dimension Gravity

2004/06/20 by Sergiu I. Vacaru
Mathematics · Physics and Astronomy · #math.DG #gr-qc #hep-th #math-ph #math.MP #msc:53Z05 #msc:83E99 #msc:83D05

paper · pdf

published as Publicationes de la Real Sociedad Matematica Espanola, 8 (2004) 104-112 · Summary of hep-th/0310132, hep-th/0310133, hep-th/0310134, to be published in Proceedings of the Conference ''Geometria de Lorentz", University of Murcia, Spain, November 12-14, 2003

arxiv created 2004/06/20 · arxiv updated 2009/12/01

Abstract

We outline a new geometric method of constructing exact solutions of gravitational field equations parametrized by generic off-diagonal metrics, anholonomic frames and possessing, in general, nontrivial torsion and nonmetricity. The formalism of nonlinear connections is elaborated for (pseudo) Riemannian and Einstein-Cartan-Weyl spaces.

Related

• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• The equations of Einstein and Cartan
• Gravity as Nonmetricity: General Relativity in Metric-Affine Space (Ln,g)
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• Some Algebraic Geometry Aspects of Gravitational Theories with Covariant and Contravariant Connections and Metrics (GTCCCM) and Possible Applications to Theories with Extra Dimensions