Perfect Fluid Spacetimes and Gradient Solitons

De, Krishnendu; De, Uday Chand; Syied, Abdallah Abdelhameed; Turki, Nasser Bin; Alsaeed, Suliman

doi:10.1007/s44198-022-00066-5

Cited by 16 publications

(4 citation statements)

References 25 publications

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“…Because of their connection to GR, there was a notable increase of quest in researching Ricci solitons and related generalizations in a variety of geometrical contexts. Many researchers have investigated many sorts of solitons in P F spacetimes including Ricci and gradient type Ricci solitons ( [17], [18]), η-Ricci solitons [4], Yamabe and gradient type Yamabe solitons [17], k-almost Yamabe solitons [15], η-Einstein solitons of gradient type [18], gradient ϱ-Einstein solitons [13], m-quasi Einstein solitons of gradient type [17], gradient Schouten solitons [18], Ricci-Yamabe solitons [14], respectively.…”

Section: Theorem C([25])mentioning

confidence: 99%

$K$-Ricci-Bourguignon Almost Solitons

De,

2024

International Electronic Journal of Geometry

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We in this current article introduce and characterize a $K$-Ricci-Bourguignon almost solitons in perfect fluid spacetimes and generalized Robertson-Walker spacetimes. First, we demonstrate that if a perfect fluid spacetime admits a $K$-Ricci-Bourguignon almost soliton, then the integral curves produced by the velocity vector field are geodesics and the acceleration vector vanishes. Then we establish that if perfect fluid spacetimes permit a gradient $K$-Ricci-Bourguignon soliton with Killing velocity vector field, then either state equation of the perfect fluid spacetime is presented by $p=\frac{3-n}{n-1}\sigma$ , or the gradient $K$-Ricci-Bourguignon soliton is shrinking or expanding under some condition. Moreover, we illustrate that the spacetime represents a perfect fluid spacetime and the divergence of the Weyl tensor vanishes if a generalized Robertson-Walker spacetime admits a $K$-Ricci-Bourguignon almost soliton.

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Section: Theorem C([25])mentioning

confidence: 99%

$K$-Ricci-Bourguignon Almost Solitons

De,

2024

International Electronic Journal of Geometry

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“…Many researchers recently examined various types of solitons in PF spacetimes, including RS ( [18] , [31] ), gradient RSs ( [31] , [32] ), Yamabe and gradient Yamabe solitons ( [32] , [33] ), gradient m-QESs [32] , gradient η -ESs [31] , gradient Schouten solitons [31] , Ricci-Yamabe solitons [34] , respectively.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

De,

Khan,

2024

Heliyon

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“…Chen [8] introduced a novel idea known as the k-almost Yamabe soliton (in short, k-AYS) in a current paper. Chen claims that if a nonzero function k, a smooth vector field Z and a smooth function λ exist such that Recently, in PF spacetimes, several researchers studied numerous type of solitons like YSs [11], gradient YSs [9], Ricci solitons ( [3], [10]), gradient Ricci solitons( [9], [10]), Ricci-Yamabe solitons [16], gradient η-Einstein solitons( [10]), gradient m-quasi…”

Section: Introductionmentioning

confidence: 99%

Perfect fluid spacetimes and $k$-almost Yamabe solitons

DE¹,

De²,

Gezer³

2023

Turkish Journal of Mathematics

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In this article, we presumed that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and creative approach, here we study k-almost yamabe solitons and gradient k-almost yamabe solitons. First, two examples are constructed to ensure the existence of gradient k-almost Yamabe solitons. Then we show that if a perfect fluid spacetime admits a k-almost yamabe soliton, then its potential vector field is Killing if and only if the divergence of the potential vector field vanishes. Besides, we prove that if a perfect fluid spacetime permit a k-almost yamabe soliton (g, k, ρ, λ), then the integral curves of the vector field ρ are geodesics, the spacetime becomes stationary and the isotopic pressure and energy density remain invariant under the velocity vector field ρ. Also, we establish that if the potential vector field is pointwise collinear with the velocity vector field and ρ(a) = 0 where a is a scalar, then either the perfect fluid spacetime represents phantom era, or the potential function Φ is invariant under the velocity vector field ρ. Finally, we prove that if a perfect fluid spacetime permits a gradient k-almost yamabe soliton (g, k, DΦ, λ) and R, λ, k are invariant under ρ, then the vorticity of the fluid vanishes.

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Perfect Fluid Spacetimes and Gradient Solitons

Cited by 16 publications

References 25 publications

$K$-Ricci-Bourguignon Almost Solitons

$K$-Ricci-Bourguignon Almost Solitons

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Perfect fluid spacetimes and $k$-almost Yamabe solitons

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