Paper · Feb 23, 2024

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons

Krishnendu De, Mohammad Nazrul Islam Khan, Uday Chand De

math.DGarXiv:2402.15339Heliyon (2024)
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Abstract

In this article, we examine gradient type Ricci solitons and -quasi Einstein solitons in generalized Robertson-Walker () spacetimes. Besides, we demonstrate that in this scenario the spacetime presents the Robertson-Walker () spacetime and the perfect fluid () spacetime presents the phantom era. Consequently, we show that if a spacetime permits a gradient - Einstein solitons, then it also represents a spacetime under certain condition.

Ricci solitonsAlmost & η-Ricci solitons

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Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Characterizations of Perfect fluid spacetimes obeying f(𝓡)-gravity equipped with different gradient solitons (Krishnendu De Young Jin Suh and Uday Chand De, 2022)1Suh 2022 Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition (Jorge Lira and Fernanda Roing, 2022)7Lira 2022 Structure of generalized Yamabe solitons and its applications (Shun Maeta, 2022)6Maeta 2022 Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes (Absos Ali Shaikh and Biswa Ranjan Datta, 2022)5Shaikh 2022 Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds (Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya, 2023)8Ghosh 2023 Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons (Krishnendu De, Uday Chand De and Aydin Gezer, 2024)2De 2024 Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection (Uday Chand De, Krishnendu De and Sinem Güler, 2024)3De 2024 η-Ricci Solitons on Kenmotsu 3-Manifolds (K. De and U. C. De, 2024)4De 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Characterizations of Perfect fluid spacetimes obeying -gravity equipped with different gradient solitons

    Krishnendu De Young Jin Suh and Uday Chand De PDF

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Uday Chand De · Shared terms “Einstein solitons”, “gradient solitons”, “perfect fluid”

  2. Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons

    Krishnendu De, Uday Chand De and Aydin Gezer PDF

    Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Krishnendu De, Uday Chand De · Shared terms “Einstein solitons”, “gradient solitons”, “gradient type”

  3. Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection

    Uday Chand De, Krishnendu De and Sinem Güler PDF

    Topics Ricci solitons · Same authors Krishnendu De, Uday Chand De · Shared terms “Robertson Walker”, “generalized Robertson”, “Walker spacetime”

  4. -Ricci Solitons on Kenmotsu 3-Manifolds

    K. De and U. C. De PDF

    Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Krishnendu De, Uday Chand De · Shared terms “Besides”

  5. Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes

    Absos Ali Shaikh and Biswa Ranjan Datta PDF

    Topics Almost & η-Ricci solitons, Ricci solitons

  6. Structure of generalized Yamabe solitons and its applications

    Shun Maeta PDF

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “gradient solitons”

  7. Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition

    Jorge Lira and Fernanda RoingWider flows PDF

    Shared terms “Robertson Walker”, “generalized Robertson”, “Walker spacetime”

  8. Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds

    Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya PDF

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Einstein solitons”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

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)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 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.