Lorentzian causality theory

IF 26.3 2区 物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS
E. Minguzzi
{"title":"Lorentzian causality theory","authors":"E. Minguzzi","doi":"10.1007/s41114-019-0019-x","DOIUrl":null,"url":null,"abstract":"<p>I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"22 1","pages":""},"PeriodicalIF":26.3000,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s41114-019-0019-x","citationCount":"85","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Living Reviews in Relativity","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s41114-019-0019-x","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 85

Abstract

I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.

Abstract Image

洛伦兹因果理论
我回顾洛伦兹的因果关系理论,特别注意所提出的结果的最优性和一般性。我包括一些在其他文献中很难找到的基本结果的完整证明(例如一些洛伦兹长度定义的等价,长度泛函的上半连续性,角正则化等)。由于对构成该理论的许多不同主题进行了系统的逻辑阐述,该论文几乎是独立的。它包含了经典概念的新结果,如最大化曲线,无时向集,边,视界,依赖域,洛伦兹距离。因果病态时空的处理需要发展一些新的通用因果关系概念,其中我发现特别方便介绍:双性性,时间等效,排列集,以及horismos和trapped集的因果版本。它们的有用性在处理经典奇点定理时变得明显,在探索一些变体和替代方案时,它在这里得到了相当大的扩展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Living Reviews in Relativity
Living Reviews in Relativity 物理-物理:粒子与场物理
CiteScore
69.90
自引率
0.70%
发文量
0
审稿时长
20 weeks
期刊介绍: Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title. Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research. Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信