A study of mixed generalized quasi-Einstein spacetimes with applications in general relativity

Mohd Bilal; Mohd Vasiulla; Abdul Haseeb; Abdullah Ali H. Ahmadini; Mohabbat Ali; Mohd Bilal; Mohd Vasiulla; Abdul Haseeb; Abdullah Ali H. Ahmadini; Mohabbat Ali

doi:10.3934/math.20231260

AIMS Mathematics

2023, Volume 8, Issue 10: 24726-24739. doi: 10.3934/math.20231260

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A study of mixed generalized quasi-Einstein spacetimes with applications in general relativity

1.
Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al Qura University, Makkah 21955, Saudi Arabia
2.
Department of Applied Sciences & Humanities, Jamia Millia Islamia (Central University), New Delhi 110025, India
3.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia

Received: 07 June 2023 Revised: 06 August 2023 Accepted: 14 August 2023 Published: 22 August 2023
MSC : 53B50, 53C25, 53C35

In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly pseudo-symmetry conditions on a mixed generalized quasi-Einstein spacetime $ MG(QE)_{4} $. Also, it is proven that if $ d\neq \varLambda $, then $ MG(QE)_{4} $ spacetime does not admit heat flux, where $ d $ and $ \varLambda $ are the function and the cosmological constant, respectively. In the end of this paper we construct a non-trivial example of $ MG(QE)_{4} $ to prove its existence.
- quasi-Einstein manifolds,
- mixed generalized quasi-Einstein manifolds,
- Einstein's field equation,
- heat flux
Citation: Mohd Bilal, Mohd Vasiulla, Abdul Haseeb, Abdullah Ali H. Ahmadini, Mohabbat Ali. A study of mixed generalized quasi-Einstein spacetimes with applications in general relativity[J]. AIMS Mathematics, 2023, 8(10): 24726-24739. doi: 10.3934/math.20231260

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Abstract

In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly pseudo-symmetry conditions on a mixed generalized quasi-Einstein spacetime $ MG(QE)_{4} $. Also, it is proven that if $ d\neq \varLambda $, then $ MG(QE)_{4} $ spacetime does not admit heat flux, where $ d $ and $ \varLambda $ are the function and the cosmological constant, respectively. In the end of this paper we construct a non-trivial example of $ MG(QE)_{4} $ to prove its existence.

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