{"title":"洛伦兹和利普希兹相遇","authors":"Christian Lange, A. Lytchak, Clemens Samann","doi":"10.4310/ATMP.2021.v25.n8.a4","DOIUrl":null,"url":null,"abstract":"We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $\\mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\\alpha$-Holder continuous Lorentzian metric admit a $\\mathcal{C}^{1,\\frac{\\alpha}{4}}$-parametrization.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"13 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Lorentz Meets Lipschitz\",\"authors\":\"Christian Lange, A. Lytchak, Clemens Samann\",\"doi\":\"10.4310/ATMP.2021.v25.n8.a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $\\\\mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\\\\alpha$-Holder continuous Lorentzian metric admit a $\\\\mathcal{C}^{1,\\\\frac{\\\\alpha}{4}}$-parametrization.\",\"PeriodicalId\":50848,\"journal\":{\"name\":\"Advances in Theoretical and Mathematical Physics\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2020-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.4310/ATMP.2021.v25.n8.a4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/ATMP.2021.v25.n8.a4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $\mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\alpha$-Holder continuous Lorentzian metric admit a $\mathcal{C}^{1,\frac{\alpha}{4}}$-parametrization.
期刊介绍:
Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.