{"title":"应用于光子表面的克鲁斯卡尔-塞克斯扩展的一些新观点","authors":"Carla Cederbaum, Markus Wolff","doi":"10.1007/s11005-024-01779-y","DOIUrl":null,"url":null,"abstract":"<div><p>It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal–Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill–Hayward to a class of spacetimes of “profile <i>h</i>” across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum–Galloway and Cederbaum–Jahns–Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01779-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Some new perspectives on the Kruskal–Szekeres extension with applications to photon surfaces\",\"authors\":\"Carla Cederbaum, Markus Wolff\",\"doi\":\"10.1007/s11005-024-01779-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal–Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill–Hayward to a class of spacetimes of “profile <i>h</i>” across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum–Galloway and Cederbaum–Jahns–Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it.\\n</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"114 2\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11005-024-01779-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01779-y\",\"RegionNum\":3,\"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":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01779-y","RegionNum":3,"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}
引用次数: 0
摘要
摘要 众所周知,施瓦兹柴尔德时空在空坐标下有一个最大的时空扩展,它将施瓦兹柴尔德外部区域延伸到基林地平线之外,称为克鲁斯卡尔-塞克斯(Kruskal-Szekeres)扩展。后来,布里尔-海沃德(Brill-Hayward)将这种扩展施瓦兹柴尔德时空的方法推广到一类跨越非退化基林视界的 "轮廓 h "时空。我们避开了他们方法中的分析微妙之处,将问题重新表述为一个 ODE,并证明了当且仅当自然产生的基林视界是非退化的时候,ODE 才有解,从而再次证实了这一事实。值得注意的是,这种方法适合讨论非光滑度量的跨视界正则性。我们将讨论光子曲面研究的应用,并将塞德鲍姆-加洛韦和塞德鲍姆-雅恩斯-维恰内克-马丁内斯的结果扩展到基林视界之外。特别是,我们的分析断言,接近基林地平线的光子表面必然会穿过基林地平线。
Some new perspectives on the Kruskal–Szekeres extension with applications to photon surfaces
It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal–Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill–Hayward to a class of spacetimes of “profile h” across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum–Galloway and Cederbaum–Jahns–Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.