Intersecting hyper-surfaces in dimensionally continued topological density gravitation

TL;DR

This paper develops a topological approach to gravity involving intersecting hypersurfaces, deriving junction conditions and localized energy tensors through characteristic classes and intersection terms.

Contribution

It introduces a novel method for formulating gravity actions with intersecting hypersurfaces using topological invariants and characteristic classes.

Findings

Derived junction conditions for intersecting hypersurfaces in topological gravity.

Established relations for intersection terms with topological significance.

Explicitly analyzed the simplest non-trivial case of the theory.

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.