2003/06/30 by Elias Gravanis, Steven Willison
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic number #Black Holes and Theoretical Physics #Boundary (topology) #Class (philosophy) #Connection (principal bundle) #General relativity #Intersection (aeronautics) #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Sequence (biology) #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1063/1.1794841
published as J.Math.Phys. 45 (2004) 4223-4238 · 20 pages, 3 figures. Accepted for Journal Math. Phys. Some minor changes and corrections
arxiv created 2004/08/25 · openalex publication_date 2004/10/23 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 localized independent energy tensors, constrained only by energy conservation. We work out explicitly the simplest nontrivial case.