Publications de l’Institut Mathématique, Nouvelle Série Vol. 103[117] 
Einstein–Hilbert Type Action on SpacetimesVladimir RovenskiDepartment of Mathematics, University of Haifa, Haifa, IsraelAbstract: The mixed gravitational field equations have been recently introduced for codimension one foliated manifolds, e.g. stably causal and globally hyperbolic spacetimes. These Euler–Lagrange equations for the total mixed scalar curvature (as analog of Einstein–Hilbert action) involve a new kind of Ricci curvature (called the mixed Ricci curvature). In the work, we derive Euler–Lagrange equations of the action for any spacetime, in fact, for a pseudoRiemannian manifold endowed with a nondegenerate distribution. The obtained equations are presented in the classical form of Einstein field equation with the new Ricci type curvature instead of Ricci curvature. Keywords: PseudoRiemannian metric, distribution, variation, mixed scalar curvature, mixed Ricci tensor, mixed gravitational field equations Classification (MSC2000): 53C12; 53C44 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.
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