Riemann Solitons on Relativistic Space-Times

IF 1.2 4区物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Gravitation and Cosmology Pub Date : 2024-08-23 DOI:10.1134/s020228932470021x

Shahroud Azami, Mehdi Jafari

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.

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相对论时空的黎曼孤子

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。

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来源期刊

Gravitation and Cosmology ASTRONOMY & ASTROPHYSICS-

CiteScore

1.70

自引率

22.20%

发文量

审稿时长

>12 weeks

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 Peoplesâ€™ 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

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