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Title: Intersecting hypersurfaces, topological densities and Lovelock Gravity
Authors: Gravanis, Elias 
Willison, Steven 
Major Field of Science: Engineering and Technology
Field Category: Civil Engineering
Keywords: Junction conditions;Lovelock gravity;Simplices
Issue Date: Aug-2007
Source: Journal of Geometry and Physics,2007, vol. 57, no. 9, pp. 1861-1882
Volume: 57
Issue: 9
Start page: 1861
End page: 1882
Journal: Journal of Geometry and Physics 
Abstract: Intersecting hypersurfaces in classical Lovelock gravity are studied exploiting the description of the Lovelock Lagrangian as a sum of dimensionally continued Euler densities. We wish to present an interesting geometrical approach to the problem. The analysis allows us to deal most efficiently with the division of space-time into a honeycomb network of cells produced by an arbitrary arrangement of membranes of matter. We write the gravitational action as bulk terms plus integrals over each lower dimensional intersection. The spin connection is discontinuous at the shared boundaries of the cells, which are spaces of various dimensionalities. That means that at each intersection there are more than one spin connections. We introduce a multi-parameter family of connections which interpolate between the different connections at each intersection. The parameters live naturally on a simplex. We can then write the action including all the intersection terms in a simple way. The Lagrangian of Lovelock gravity is generalized so as to live on the simplices as well. Each intersection term of the action is then obtained as an integral over an appropriate simplex. Lovelock gravity and the associated topological (Euler) density are used as an example of a more general formulation. In this example one finds that singular sources up to a certain co-dimensionality naturally carry matter without introducing conical or other singularities in spacetime geometry.
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2007.03.005
Rights: © Elsevier
Type: Article
Affiliation : King's College London 
Centro de Estudios Científicos (CECS) 
Cyprus University of Technology 
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