IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i18p2209-d631985.html
   My bibliography  Save this article

A Characterization of GRW Spacetimes

Author

Listed:
  • Ibrahim Al-Dayel

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, P.O. Box 65892, Riyadh 11566, Saudi Arabia)

  • Sharief Deshmukh

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mohd. Danish Siddiqi

    (Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia)

Abstract

We show presence a special torse-forming vector field (a particular form of torse-forming of a vector field) on generalized Robertson–Walker (GRW) spacetime, which is an eigenvector of the de Rham–Laplace operator. This paves the way to showing that the presence of a time-like special torse-forming vector field ξ with potential function ρ on a Lorentzian manifold ( M , g ) , dim M > 5 , which is an eigenvector of the de Rham Laplace operator, gives a characterization of a GRW-spacetime. We show that if, in addition, the function ξ ( ρ ) is nowhere zero, then the fibers of the GRW-spacetime are compact. Finally, we show that on a simply connected Lorentzian manifold ( M , g ) that admits a time-like special torse-forming vector field ξ , there is a function f called the associated function of ξ . It is shown that if a connected Lorentzian manifold ( M , g ) , dim M > 4 , admits a time-like special torse-forming vector field ξ with associated function f nowhere zero and satisfies the Fischer–Marsden equation, then ( M , g ) is a quasi-Einstein manifold.

Suggested Citation

  • Ibrahim Al-Dayel & Sharief Deshmukh & Mohd. Danish Siddiqi, 2021. "A Characterization of GRW Spacetimes," Mathematics, MDPI, vol. 9(18), pages 1-9, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2209-:d:631985
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/18/2209/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/18/2209/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2209-:d:631985. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.