Investigation on gradient solitons in perfect fluid spacetimes

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Krishnendu De, Uday Chand De
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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.

理想流体时空中梯度孤子的研究
本文研究了具有不同类型梯度孤子的完美流体时空。证明了在具有kill速度矢量的完美流体时空中,如果存在梯度型τ-爱因斯坦孤子,则该时空表示虚区,或者ψ在速度矢量场ρ下保持不变。此外,我们还建立了在具有恒定标量曲率的完美流体时空中,如果洛伦兹度规是梯度τ-爱因斯坦孤子,则要么τ-爱因斯坦梯度势函数与ρ点共线,要么时空代表刚性物质流体。进一步证明了在一定条件下,完美流体时空可以转化为广义的Robertson-Walker时空和静态时空,这种时空为Petrov型I、D或o。我们还刻画了完美流体时空的洛伦兹度规具有梯度m-准爱因斯坦孤子,并且完美流体时空具有消失的膨胀标量,或者在一定的势函数限制下代表暗能量时代。
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来源期刊
Reports on Mathematical Physics
Reports on Mathematical Physics 物理-物理:数学物理
CiteScore
1.80
自引率
0.00%
发文量
40
审稿时长
6 months
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.
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