{"title":"Riemann Solitons on Relativistic Space-Times","authors":"Shahroud Azami, Mehdi Jafari","doi":"10.1134/S020228932470021X","DOIUrl":null,"url":null,"abstract":"<p>We examine almost Riemann solitons and almost gradient Riemann solitons in generalized Robertson–Walker space-times and perfect fluid space-times. At first, we prove that if a generalized Robertson–Walker space-time admits an almost Riemann soliton or an almost gradient Riemann soliton, then it becomes a perfect fluid space-time. Next, we observe that a space-time with an almost Riemann soliton whose potential vector field, is a conformal vector field, is an Einstein manifold, and if the potential vector field is a nonhomothetic conformal vector field, then space-time is of Petrov type O or N. In final, we prove that if a generalized Robertson–Walker space-time satisfies the definition of an almost Riemann soliton, and <span>\\(Q.P=0\\)</span> then it is an Einstein manifold, and consequently it is a perfect fluid space-time.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"30 3","pages":"306 - 311"},"PeriodicalIF":1.2000,"publicationDate":"2024-08-23","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/S020228932470021X","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
We examine almost Riemann solitons and almost gradient Riemann solitons in generalized Robertson–Walker space-times and perfect fluid space-times. At first, we prove that if a generalized Robertson–Walker space-time admits an almost Riemann soliton or an almost gradient Riemann soliton, then it becomes a perfect fluid space-time. Next, we observe that a space-time with an almost Riemann soliton whose potential vector field, is a conformal vector field, is an Einstein manifold, and if the potential vector field is a nonhomothetic conformal vector field, then space-time is of Petrov type O or N. In final, we prove that if a generalized Robertson–Walker space-time satisfies the definition of an almost Riemann soliton, and \(Q.P=0\) then it is an Einstein manifold, and consequently it is a perfect fluid space-time.
摘要 我们研究广义罗伯逊-沃克时空和完美流体时空中的近黎曼孤子和近梯度黎曼孤子。首先，我们证明，如果广义罗伯逊-沃克时空中存在几乎黎曼孤子或几乎梯度黎曼孤子，那么它就成为完美流体时空。接下来，我们观察到，一个具有几乎黎曼孤子的时空，如果其势能向量场是共形向量场，那么它就是爱因斯坦流形；如果势能向量场是非同调共形向量场，那么它就是彼得罗夫 O 或 N 型时空。最后，我们证明，如果广义罗伯逊-沃克时空满足几乎黎曼孤子的定义，并且（Q.P=0\），那么它就是爱因斯坦流形，因此它是完美流体时空。
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
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
