Paper · Feb 7, 2022

Characterizations of Perfect fluid spacetimes obeying $f (R)$ -gravity equipped with different gradient solitons

Krishnendu De Young Jin Suh, Uday Chand De

math.DGarXiv:2202.03254v2International Journal of Geometric Methods in Modern Physics Vol. 20, No. 10 (2023) 2350174 (15 pages)

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Abstract

The prime object of this article is to study the perfect fluid spacetimes obeying $f (R)$ -gravity, when $η$ -Ricci solitons, gradient $η$ -Ricci solitons, gradient Einstein Solitons and gradient $m$ -quasi Einstein solitons are its metrics. At first, the existence of the $η$ -Ricci solitons is proved by a non-trivial example. We establish conditions for which the $η$ -Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying $f (R)$ -gravity, when the potential vector field of $η$ -Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient $η$ -Ricci solitons, gradient Einstein Solitons and gradient $m$ -quasi Einstein solitons in $f (R)$ -gravity, respectively. As a result, we establish some significant theorems about dark matter era.

Comments: 19

Ricci solitons Almost & η-Ricci solitons Physics

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Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

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11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.

Characterizations of Perfect fluid spacetimes obeying $f (R)$ -gravity equipped with different gradient solitons

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Characterizations of Perfect fluid spacetimes obeying f(R)-gravity equipped with different gradient solitons

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Characterizations of Perfect fluid spacetimes obeying $f (R)$ -gravity equipped with different gradient solitons