{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":"613 ","pages":""},"PeriodicalIF":17.7000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2023-0256","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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