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Title: Singular sources in gravity and homotopy in the space of connections
Authors: Gravanis, Elias 
Willison, Steven 
Major Field of Science: Natural Sciences
Field Category: Physical Sciences
Keywords: Gravitation;Algebra;Cosmological constant
Issue Date: Dec-2009
Source: Journal of Mathematical Physics, 2009, vol. 50, no. 12, pp. 122505-1-122505-32
Volume: 50
Issue: 12
Start page: 122505-1
End page: 122505-32
Journal: Journal of Mathematical Physics 
Abstract: Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a distribution, depending on whether there is some undefined product of distributions. Supposing that the Lagrangian is a distribution, it is unambiguously defined as the limit of a sequence of Lagrangians. But there still remains the question: Is the distributional Lagrangian uniquely defined by the limiting process for the fields themselves? In this paper a general geometrical construction is advanced to address this question. We describe certain types of singularities, not by distribution valued tensors, but by showing that the action functional for the singular fields is (formally) equivalent to another action built out of \emph{smooth} fields. Thus we manage to make the problem of the lack of a derivative disappear from a system which gives differential equations. Certain ideas from homotopy and homology theory turn out to be of central importance in analyzing the problem and clarifying finer aspects of it. The method is applied to general relativity in first order formalism, which gives some interesting insights into distributional geometries in that theory. Then more general gravitational Lagrangians in first order formalism are considered such as Lovelock terms (for which the action principle admits space-times more singular than other higher curvature theories).
ISSN: 10897658
DOI: 10.1063/1.3250196
Rights: © American Institute of Physics
Type: Article
Affiliation : Centro de Estudios Científicos (CECS) 
Cyprus University of Technology 
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