Hyperbolic Ricci solitons on perfect fluid spacetimes

Shahroud Azami; Mehdi Jafari; Nargis Jamal; Abdul Haseeb; Shahroud Azami; Mehdi Jafari; Nargis Jamal; Abdul Haseeb

doi:10.3934/math.2024921

AIMS Mathematics

2024, Volume 9, Issue 7: 18929-18943. doi: 10.3934/math.2024921

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Hyperbolic Ricci solitons on perfect fluid spacetimes

1.
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
2.
Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran
3.
Department of Mathematics, College of Science (Girls Campus Mahliya), Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
4.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia

Received: 07 April 2024 Revised: 24 May 2024 Accepted: 29 May 2024 Published: 05 June 2024
MSC : 53C25, 53C50, 53E20, 83C05

In the present paper, we investigate perfect fluid spacetimes and perfect fluid generalized Roberston-Walker spacetimes that contain a torse-forming vector field satisfying almost hyperbolic Ricci solitons. We show that the perfect fluid spacetimes that contain a torse-forming vector field satisfy an almost hyperbolic Ricci soliton, and we prove that a perfect fluid generalized Roberston-Walker spacetime satisfying an almost hyperbolic Ricci soliton $ (g, \zeta, \varrho, \mu) $ is an Einstein manifold. Also, we study an almost hyperbolic Ricci soliton $ (g, V, \varrho, \mu) $ on these spacetimes when $ V $ is a conformal vector field, a torse-forming vector field, or a Ricci bi-conformal vector field.
- perfect fluid spacetimes,
- hyperbolic Ricci solitons,
- Einstein manifolds
Citation: Shahroud Azami, Mehdi Jafari, Nargis Jamal, Abdul Haseeb. Hyperbolic Ricci solitons on perfect fluid spacetimes[J]. AIMS Mathematics, 2024, 9(7): 18929-18943. doi: 10.3934/math.2024921

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Abstract

In the present paper, we investigate perfect fluid spacetimes and perfect fluid generalized Roberston-Walker spacetimes that contain a torse-forming vector field satisfying almost hyperbolic Ricci solitons. We show that the perfect fluid spacetimes that contain a torse-forming vector field satisfy an almost hyperbolic Ricci soliton, and we prove that a perfect fluid generalized Roberston-Walker spacetime satisfying an almost hyperbolic Ricci soliton $ (g, \zeta, \varrho, \mu) $ is an Einstein manifold. Also, we study an almost hyperbolic Ricci soliton $ (g, V, \varrho, \mu) $ on these spacetimes when $ V $ is a conformal vector field, a torse-forming vector field, or a Ricci bi-conformal vector field.

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