Hyperbolic Ricci soliton and gradient hyperbolic Ricci soliton on relativistic prefect fluid spacetime

Mohd. Danish Siddiqi; Fatemah Mofarreh; Mohd. Danish Siddiqi; Fatemah Mofarreh

doi:10.3934/math.20241051

AIMS Mathematics

2024, Volume 9, Issue 8: 21628-21640. doi: 10.3934/math.20241051

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Research article

Hyperbolic Ricci soliton and gradient hyperbolic Ricci soliton on relativistic prefect fluid spacetime

Mohd. Danish Siddiqi ^{1
,
,},
Fatemah Mofarreh ^{2
,
,}

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi Arabia
2.
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia

Received: 21 April 2024 Revised: 11 June 2024 Accepted: 14 June 2024 Published: 05 July 2024
MSC : 53B30, 53C44, 53C50, 53C80

In this research note, we investigated the characteristics of perfect fluid spacetime when coupled with the hyperbolic Ricci soliton. We additionally interacted with the perfect fluid spacetime, with a $ \varphi(\mathcal{Q}) $-vector field and a bi-conformal vector field that admits the hyperbolic Ricci solitons. Furthermore, we analyze the gradient hyperbolic Ricci soliton in perfect fluid spacetime, employing a scalar concircular field, and discuss about the gradient hyperbolic Ricci soliton's rate of change. In the end, we determined the energy conditions for perfect fluid spacetime in terms of gradient hyperbolic Ricci soliton with a scalar concircular field.
- perfect fluid spacetime,
- hyperbolic Ricci solitons,
- gradient hyperbolic Ricci soliton,
- Bi-conformal vector field,
- scalar concircular field,
- energy condition
Citation: Mohd. Danish Siddiqi, Fatemah Mofarreh. Hyperbolic Ricci soliton and gradient hyperbolic Ricci soliton on relativistic prefect fluid spacetime[J]. AIMS Mathematics, 2024, 9(8): 21628-21640. doi: 10.3934/math.20241051

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Abstract

In this research note, we investigated the characteristics of perfect fluid spacetime when coupled with the hyperbolic Ricci soliton. We additionally interacted with the perfect fluid spacetime, with a $ \varphi(\mathcal{Q}) $-vector field and a bi-conformal vector field that admits the hyperbolic Ricci solitons. Furthermore, we analyze the gradient hyperbolic Ricci soliton in perfect fluid spacetime, employing a scalar concircular field, and discuss about the gradient hyperbolic Ricci soliton's rate of change. In the end, we determined the energy conditions for perfect fluid spacetime in terms of gradient hyperbolic Ricci soliton with a scalar concircular field.

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