Intersecting hyper-surfaces in dimensionally continued topological density gravitation

Abstract

We consider intersecting hypersurfaces in curved spacetime with gravity governed by a class of actions which are topological invariants in lower dimensionality. Along with the Chern-Simons boundary terms there is a sequence of intersection terms that should be added in the action functional for a well defined variational principle. We construct them in the case of Characteristic Classes, obtaining relations which have a general topological meaning. Applying them on a manifold with a discontinuous connection 1-form we obtain the gravity action functional of the system and show that the junction conditions can be found in a simple algebraic way. At the sequence of intersections there are localised independent energy tensors, constrained only by energy conservation. We work out explicitly the simplest non trivial case.

20 pages, 3 figures. Accepted for Journal Math. Phys. Some minor changes and corrections

References in corpus (4)

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• Intersecting hypersurfaces, topological densities and Lovelock Gravity
• Shock waves and Birkhoff's theorem in Lovelock gravity
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• Conserved charges in (Lovelock) gravity in first order formalism
• Singular sources in gravity and homotopy in the space of connections