2009
DOI: 10.1063/1.3250196
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Singular sources in gravity and homotopy in the space of connections

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… Show more

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Cited by 6 publications
(11 citation statements)
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“…In the lightlike limit (H → ∞), we get a consistent equation for H either if a → ∞ and H ∼ a d−1 or M + → M − , which coincides with the result of [34]. In the former case, the asymptotic behavior of the potential reads…”
Section: Fate Of the Bubblessupporting
confidence: 80%
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“…In the lightlike limit (H → ∞), we get a consistent equation for H either if a → ∞ and H ∼ a d−1 or M + → M − , which coincides with the result of [34]. In the former case, the asymptotic behavior of the potential reads…”
Section: Fate Of the Bubblessupporting
confidence: 80%
“…To this end, we will split the geometry as M = M − ∪ (Σ × ξ) ∪ M + , where M ∓ denote the interior/exterior regions respectively, Σ is the codimension one junction (hyper)surface, and ξ ∈ [0, 1] is a real segment/parameter used to interpolate both regions. 3 The matching condition can be obtained from an action principle constructed by means of two auxiliary quantities [34]…”
Section: Junction Conditionsmentioning
confidence: 99%
“…The limit we described here as ∆ → Σ, or any limit equivalent to it, was studied for any theory built out of forms fields alone, such as E and ω, in Ref. [50]. The general result is as follows.…”
Section: B Manufacturing a Discontinuitymentioning
confidence: 99%
“…To do this we shall exploit the formulation of matching conditions first presented in Ref. [48] and further elaborated in [49] and [50]. The basic facts of the method can be summarized as follows.…”
Section: Introductionmentioning
confidence: 99%
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