(Pseudo)Generalized Kaluza-Klein G-Spaces and Einstein Equations

Abstract

Introducing the Lie algebroid generalized tangent bundle of a Kaluza-Klein bundle, we develop the theory of general distinguished linear connections for this space. In particular, using the Lie algebroid generalized tangent bundle of the Kaluza-Klein vector bundle, we present the $\left(g,h\right)$-lift of a curve on the base $M$ and we characterize the horizontal and vertical parallelism of the $\left(g,h\right)$-lift of accelerations with respect to a distinguished linear $\left(\rho ,\eta \right)$-connection. Moreover, we study the torsion, curvature and Ricci tensor field associated to a distinguished linear $\left(\rho ,\eta \right)$-connection and we obtain the identities of Cartan and Bianchi type in the general framework of the Lie algebroid generalized tangent bundle of a Kaluza-Klein bundle. Finally, we introduce the theory of (pseudo) generalized Kaluza-Klein G-spaces and we develop the Einstein equations in this general framework.

29 pages. arXiv admin note: text overlap with arXiv:1007.1541

References in corpus (4)

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• Einstein-Cartan Algebroids and Black Holes in Solitonic Backgrounds
• The generalized Lie algebroids and their applications
• Clifford Algebroids and Nonholonomic Spinor Deformations of Taub-NUT Spacetimes