{"title":"带辐射源的 2+1 维空面公式解法","authors":"T. Harriott, J. G. Williams","doi":"10.1139/cjp-2023-0256","DOIUrl":null,"url":null,"abstract":"The null-surface formulation (NSF) of general relativity has three coupled and highly nonlinear eld equations whose solution determines (a family of) null surfaces indicated by the variable u. This variable is one of a set of intrinsic coordinates that are defined in terms of the surfaces. The first of the three field equations is called the main metricity condition, and it is by far the most complicated. This work considers the NSF in 2+1 dimensions and presents a solution that is founded on the following strategy: Simplify the main metricity condition by requiring the uu-component of the metric tensor to be zero and then search for an additively separable solution formed from a sum of separate terms, each term being linked with a term in a certain differential operator ∂ so as to cause a convenient cancellation. The main motivation for this approach is that it may suggest how to find a solution in higher dimensions, where the role of ∂ is played by the eth operator of Newman and Penrose.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution for the null-surface formulation in 2+1 dimensions with radiation source\",\"authors\":\"T. Harriott, J. G. Williams\",\"doi\":\"10.1139/cjp-2023-0256\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The null-surface formulation (NSF) of general relativity has three coupled and highly nonlinear eld equations whose solution determines (a family of) null surfaces indicated by the variable u. This variable is one of a set of intrinsic coordinates that are defined in terms of the surfaces. The first of the three field equations is called the main metricity condition, and it is by far the most complicated. This work considers the NSF in 2+1 dimensions and presents a solution that is founded on the following strategy: Simplify the main metricity condition by requiring the uu-component of the metric tensor to be zero and then search for an additively separable solution formed from a sum of separate terms, each term being linked with a term in a certain differential operator ∂ so as to cause a convenient cancellation. The main motivation for this approach is that it may suggest how to find a solution in higher dimensions, where the role of ∂ is played by the eth operator of Newman and Penrose.\",\"PeriodicalId\":9413,\"journal\":{\"name\":\"Canadian Journal of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1139/cjp-2023-0256\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2023-0256","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
广义相对论的空面公式(NSF)有三个高度非线性的耦合长方程,其解法决定了由变量 u 表示的(一系列)空面。三个场方程中的第一个被称为主要度量条件,也是迄今为止最复杂的一个。本研究考虑了 2+1 维的 NSF,并提出了基于以下策略的解决方案:通过要求度量张量的 uu 分量为零来简化主度量条件,然后寻找一个由独立项之和组成的可加可分的解,每个项都与某个微分算子 ∂ 中的一个项相关联,以便于抵消。采用这种方法的主要动机是,它可以提出如何在更高维度中找到解,在更高维度中,∂的作用由纽曼和彭罗斯的乙算子扮演。
Solution for the null-surface formulation in 2+1 dimensions with radiation source
The null-surface formulation (NSF) of general relativity has three coupled and highly nonlinear eld equations whose solution determines (a family of) null surfaces indicated by the variable u. This variable is one of a set of intrinsic coordinates that are defined in terms of the surfaces. The first of the three field equations is called the main metricity condition, and it is by far the most complicated. This work considers the NSF in 2+1 dimensions and presents a solution that is founded on the following strategy: Simplify the main metricity condition by requiring the uu-component of the metric tensor to be zero and then search for an additively separable solution formed from a sum of separate terms, each term being linked with a term in a certain differential operator ∂ so as to cause a convenient cancellation. The main motivation for this approach is that it may suggest how to find a solution in higher dimensions, where the role of ∂ is played by the eth operator of Newman and Penrose.
期刊介绍:
The Canadian Journal of Physics publishes research articles, rapid communications, and review articles that report significant advances in research in physics, including atomic and molecular physics; condensed matter; elementary particles and fields; nuclear physics; gases, fluid dynamics, and plasmas; electromagnetism and optics; mathematical physics; interdisciplinary, classical, and applied physics; relativity and cosmology; physics education research; statistical mechanics and thermodynamics; quantum physics and quantum computing; gravitation and string theory; biophysics; aeronomy and space physics; and astrophysics.