Generalizations of the Abstract Boundary singularity theorem

The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give...

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Bibliographic Details
Published in:arXiv.org 2015-08
Main Authors: Whale, Ben E, Mike J S L Ashley, Scott, Susan M
Format: Article
Language:English
Subjects:
Existence theorems
Geodesy
Singularities
Online Access:Get full text
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Summary:The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from \(C^1\) curves to locally Lipschitz curves.
ISSN:2331-8422
DOI:10.48550/arxiv.1508.04602