O. V. Babourova, B. N. Frolov, M. S. Khetczeva, D. V. Kushnir
{"title":"Trautman Problem and its Solution for Plane Waves in Riemann and Riemann–Cartan Spaces","authors":"O. V. Babourova, B. N. Frolov, M. S. Khetczeva, D. V. Kushnir","doi":"10.1134/S0202289323020044","DOIUrl":null,"url":null,"abstract":"<p>The Trautman problem determines the conditions under which GWs transfer the information contained in them in an invariant manner. According to the analogy between plane gravitational and electromagnetic waves, the metric tensor of a plane gravitational wave is invariant under the five-dimensional group <span>\\(G_{5}\\)</span>, which does not change the null hypersurface of the plane wave front. The theorems are proven on the equality to zero for the result of the action of the Lie derivative on the curvature 2-form of a plane GW in Riemann and Riemann–Cartan spaces in the direction determined by the vector generating the group <span>\\(G_{5}\\)</span>. Thus the curvature tensor of a plane gravitational wave can invariantly transfer the information encoded in the source of the GW.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"29 2","pages":"103 - 109"},"PeriodicalIF":1.2000,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289323020044","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
The Trautman problem determines the conditions under which GWs transfer the information contained in them in an invariant manner. According to the analogy between plane gravitational and electromagnetic waves, the metric tensor of a plane gravitational wave is invariant under the five-dimensional group \(G_{5}\), which does not change the null hypersurface of the plane wave front. The theorems are proven on the equality to zero for the result of the action of the Lie derivative on the curvature 2-form of a plane GW in Riemann and Riemann–Cartan spaces in the direction determined by the vector generating the group \(G_{5}\). Thus the curvature tensor of a plane gravitational wave can invariantly transfer the information encoded in the source of the GW.
期刊介绍:
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community