Paper · Sep 7, 2017

Kinematic Description of Ricci Solitons in Fluid Spacetimes

Umber Sheikh

gr-qcarXiv:1709.02138v2
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Abstract

We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.

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Submitted
Sep 7, 2017
Last revised
Jan 11, 2018 (v2)
Subjects
gr-qc, math.DG

Comments: 13 pages, no figure

Ricci solitonsRotational symmetry & warped products

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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 Solitons and geometrical structures in a perfect fluid spacetime (Adara M. Blaga, 2017)1Blaga 2017 Harmonic aspects in an η-Ricci soliton (Adara M. Blaga, 2018)7Blaga 2018 Existence of hypercylinder expanders of the inverse mean curvature flow (K. M. Hui, 2018)8Hui 2018 Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field (Venkatesha and Aruna Kumara H, 2018)3Venkatesha 2018 Perfect fluid spacetimes and gradient solitons (Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al., 2021)2De 2021 On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization (Abbas M Sherif, Peter K S Dunsby and Rituparno Goswami, 2021)6Sherif 2021 Characterizations of Perfect fluid spacetimes obeying f(𝓡)-gravity equipped with different gradient solitons (Krishnendu De Young Jin Suh and Uday Chand De, 2022)4Suh 2022 Almost Gradient Ricci Solitons on Static Spacetime (Akhilesh Yadav and Tarun Saxena, 2025)5Yadav 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Solitons and geometrical structures in a perfect fluid spacetime

    Adara M. Blaga

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  2. Perfect fluid spacetimes and gradient solitons

    Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al.

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  3. Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field

    Venkatesha and Aruna Kumara H

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  4. Characterizations of Perfect fluid spacetimes obeying -gravity equipped with different gradient solitons

    Krishnendu De Young Jin Suh and Uday Chand De

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  5. Almost Gradient Ricci Solitons on Static Spacetime

    Akhilesh Yadav and Tarun Saxena

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “spacetime admitting”

  6. On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization

    Abbas M Sherif, Peter K S Dunsby and Rituparno Goswami

    Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “spacetime admitting”, “physical”

  7. Harmonic aspects in an -Ricci soliton

    Adara M. Blaga

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  8. Existence of hypercylinder expanders of the inverse mean curvature flow

    K. M. Hui

    Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “radially symmetric”

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) Rotational symmetry & warped products For rotationally symmetric metrics and warped products, Ricci flow reduces to a parabolic equation in one space variable. Start with: The ricci flow on radially symmetric R3 (Ivey, 1994)

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.