Investigations on solitons in $$f({\mathcal {R}})$$-gravity

De, Krishnendu; De, Uday Chand

doi:10.1140/epjp/s13360-022-02399-y

Cited by 12 publications

(4 citation statements)

References 19 publications

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“…Buchdahl proposed the aforementioned hypothesis [6] and Starobinsky [27] has accomplished viability with the study of cosmic inflation. In earlier works, a number of useful functional forms of f (R) were presented in ( [7], [8], [9], [14], [15], [18]).…”

Section: Introductionmentioning

confidence: 99%

Ricci-Yamabe Solitons in f(R)-gravity

2023

International Electronic Journal of Geometry

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The main objective of this paper is to describe the perfect fluid spacetimes fulfilling $f(R)$-gravity, when Ricci-Yamabe, gradient Ricci-Yamabe and $\eta$-Ricci-Yamabe solitons are its metrics. We acquire conditions for which the Ricci-Yamabe and the gradient Ricci-Yamabe solitons are expanding, steady or shrinking. Furthermore, we investigate $\eta$-Ricci-Yamabe solitons and deduce a Poisson equation and with the help of this equation, we acquire some significant results.

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Section: Introductionmentioning

confidence: 99%

Ricci-Yamabe Solitons in f(R)-gravity

2023

International Electronic Journal of Geometry

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“…[ 5 ] Of course, various theoretical scalar‐tensor findings and observational data, constrain the feasibility of such functions. Many useful functional versions of

\mathcal {F}(\mathcal {R})

theory have been developed recently; for additional information, see ( [ 6,12,14,16,17 ] ). By the motivation of these investigations, in this article we concentrate on a

(QC)_4

‐ spacetime solution in

\mathcal {F}(\mathcal {R})

‐gravity and prove the following main results.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of a Spacetime of Quasi‐Constant Sectional Curvature and F(R)$\mathcal {F}(\mathcal {R})$‐Gravity

Zengin

et al. 2023

Fortschritte der Physik

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The main aim of this article is to investigate a spacetime of quasi-constant sectional curvature. At first, the existence of such a spacetime is established by several examples. We have shown that a spacetime of quasi-constant sectional curvature agrees with the present state of the universe and it represents a Robertson Walker spacetime. Moreover, if the spacetime is Ricci semi-symmetric or Ricci symmetric, then either the spacetime represents a spacetime of constant sectional curvature, or the spacetime represents phantom era. Also, we prove that a Ricci symmetric spacetime of quasi-constant sectional curvature represents a static spacetime and the spacetime under consideration is of Petrov type I, D or O. Finally, we concentrate on a quasi-constant sectional curvature spacetime solution in  ()-gravity. As a result, various energy conditions are studied and analyzed our obtained outcomes in terms of a  ()-gravity model.

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“…The study of Ricci solitons is not limited to the general theory of relativity and many authors have discussed it in the modified theories of gravity. Krishnadu Chand [23] investigated Ricci solitons in f (R) gravity theory for perfect fluid and constant Ricci scalar spacetime. They also discussed gradient Ricci solitons and gradient Yamabe solitons in f (R) gravity theory.…”

Section: Introductionmentioning

confidence: 99%

Ricci solitons on anisotropic fluid spacetime in f(R, T)-gravity

Khan,

Ali,

Gul

2023

Phys. Scr.

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In this paper we study the behaviour of anisotropic ﬂuid spacetimes in f(R, T )-gravity for admitting Ricci Soliton. We obtain the form of tangential pressure of the ﬂuid for steady, shrinking and expanding Ricci soliton when Ricci soliton vector ﬁeld becomes a Killing vector ﬁeld. Modiﬁed Poisson and Liouville equations are derived from the Ricci soliton equation in f(R, T )-gravity having anisotropic ﬂuid. Also harmonic signiﬁcance of Ricci soliton on anisotropic ﬂuid spacetime in f(R, T )-gravity with a harmonic potential function is derived. We derive ﬁeld equations for perfect ﬂuid plane symmetric static spacetime and obtain their solutions. For each solution we then obtain Ricci soliton vector ﬁelds. We observe that such spacetimes admit expanding, shrinking or steady Ricci solitons. All the obtained solitons are trivial in nature. When these Ricci soliton vector ﬁelds become Killing vector ﬁelds then our results are in full agreement with the theorems deduced from our study.

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Investigations on solitons in $$f({\mathcal {R}})$$-gravity

Cited by 12 publications

References 19 publications

Ricci-Yamabe Solitons in f(R)-gravity

Ricci-Yamabe Solitons in f(R)-gravity

Characterizations of a Spacetime of Quasi‐Constant Sectional Curvature and F(R)$\mathcal {F}(\mathcal {R})$‐Gravity

Ricci solitons on anisotropic fluid spacetime in f(R, T)-gravity

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