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...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Whale, Ben E
Mike J S L Ashley
Scott, Susan M
description 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.
doi_str_mv 10.48550/arxiv.1508.04602
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2083184694</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2083184694</sourcerecordid><originalsourceid>FETCH-LOGICAL-a524-847838e5ab9485485a8005028515c759a258a1960056135bb163e4956e3f1db13</originalsourceid><addsrcrecordid>eNotjk9LAzEUxIMgWGo_gLcFz7u-_HnZBLzUolUoeOm9vG2zmrImmmTF-uldURgYGIb5DWNXHBplEOGG0pf_bDiCaUBpEGdsJqTktVFCXLBFzkcAELoViHLGbtcuuESD_6biY8hV7Kvy6qpll0uifanu4hgOlE5V9uFlHCj5cvptxOTeLtl5T0N2i3-fs-3D_Xb1WG-e10-r5aYmFGoCt0Yah9TZ6eEkMgAIwiDHfYuWBBriVk-h5hK7jmvplEXtZM8PHZdzdv03-57ix-hy2R3jmMJE3AkwkhulrZI_1hNH6Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2083184694</pqid></control><display><type>article</type><title>Generalizations of the Abstract Boundary singularity theorem</title><source>Publicly Available Content Database</source><creator>Whale, Ben E ; Mike J S L Ashley ; Scott, Susan M</creator><creatorcontrib>Whale, Ben E ; Mike J S L Ashley ; Scott, Susan M</creatorcontrib><description>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.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1508.04602</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Existence theorems ; Geodesy ; Singularities</subject><ispartof>arXiv.org, 2015-08</ispartof><rights>2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2083184694?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>778,782,25736,27908,36995,44573</link.rule.ids></links><search><creatorcontrib>Whale, Ben E</creatorcontrib><creatorcontrib>Mike J S L Ashley</creatorcontrib><creatorcontrib>Scott, Susan M</creatorcontrib><title>Generalizations of the Abstract Boundary singularity theorem</title><title>arXiv.org</title><description>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.</description><subject>Existence theorems</subject><subject>Geodesy</subject><subject>Singularities</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNotjk9LAzEUxIMgWGo_gLcFz7u-_HnZBLzUolUoeOm9vG2zmrImmmTF-uldURgYGIb5DWNXHBplEOGG0pf_bDiCaUBpEGdsJqTktVFCXLBFzkcAELoViHLGbtcuuESD_6biY8hV7Kvy6qpll0uifanu4hgOlE5V9uFlHCj5cvptxOTeLtl5T0N2i3-fs-3D_Xb1WG-e10-r5aYmFGoCt0Yah9TZ6eEkMgAIwiDHfYuWBBriVk-h5hK7jmvplEXtZM8PHZdzdv03-57ix-hy2R3jmMJE3AkwkhulrZI_1hNH6Q</recordid><startdate>20150819</startdate><enddate>20150819</enddate><creator>Whale, Ben E</creator><creator>Mike J S L Ashley</creator><creator>Scott, Susan M</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20150819</creationdate><title>Generalizations of the Abstract Boundary singularity theorem</title><author>Whale, Ben E ; Mike J S L Ashley ; Scott, Susan M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a524-847838e5ab9485485a8005028515c759a258a1960056135bb163e4956e3f1db13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Existence theorems</topic><topic>Geodesy</topic><topic>Singularities</topic><toplevel>online_resources</toplevel><creatorcontrib>Whale, Ben E</creatorcontrib><creatorcontrib>Mike J S L Ashley</creatorcontrib><creatorcontrib>Scott, Susan M</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Whale, Ben E</au><au>Mike J S L Ashley</au><au>Scott, Susan M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalizations of the Abstract Boundary singularity theorem</atitle><jtitle>arXiv.org</jtitle><date>2015-08-19</date><risdate>2015</risdate><eissn>2331-8422</eissn><abstract>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.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1508.04602</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2015-08
issn 2331-8422
language eng
recordid cdi_proquest_journals_2083184694
source Publicly Available Content Database
subjects Existence theorems
Geodesy
Singularities
title Generalizations of the Abstract Boundary singularity theorem
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T22%3A35%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Generalizations%20of%20the%20Abstract%20Boundary%20singularity%20theorem&rft.jtitle=arXiv.org&rft.au=Whale,%20Ben%20E&rft.date=2015-08-19&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1508.04602&rft_dat=%3Cproquest%3E2083184694%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a524-847838e5ab9485485a8005028515c759a258a1960056135bb163e4956e3f1db13%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2083184694&rft_id=info:pmid/&rfr_iscdi=true