{"title":"Investigation on gradient solitons in perfect fluid spacetimes","authors":"Krishnendu De, Uday Chand De","doi":"10.1016/S0034-4877(23)00035-6","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing </span>velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or </span><em>ψ</em><span><span> remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant scalar curvature<span>, if the Lorentzian metric is the gradient τ-Einstein soliton, then either the τ-Einstein gradient potential function is pointwise<span> collinear with ρ, or the spacetime represents stiff matter fluid. Furthermore, we prove that under certain conditions, a perfect fluid spacetime turns into a generalized Robertson–Walker spacetime, as well as a </span></span></span>static spacetime and such a spacetime is of Petrov type I, D or O. We also characterize perfect fluid spacetimes whose Lorentzian metric is equipped with gradient </span><em>m</em><span>-quasi Einstein solitons and that the perfect fluid spacetime has vanishing expansion scalar, or it represents dark energy era under certain restriction on the potential function.</span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487723000356","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or ψ remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant scalar curvature, if the Lorentzian metric is the gradient τ-Einstein soliton, then either the τ-Einstein gradient potential function is pointwise collinear with ρ, or the spacetime represents stiff matter fluid. Furthermore, we prove that under certain conditions, a perfect fluid spacetime turns into a generalized Robertson–Walker spacetime, as well as a static spacetime and such a spacetime is of Petrov type I, D or O. We also characterize perfect fluid spacetimes whose Lorentzian metric is equipped with gradient m-quasi Einstein solitons and that the perfect fluid spacetime has vanishing expansion scalar, or it represents dark energy era under certain restriction on the potential function.
期刊介绍:
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.