Investigation of Pseudo-Ricci Symmetric Spacetimes in Gray’s Subspaces

Shenawy, Sameh; De, Uday Chand; Turki, Nasser Bin; Alsaeed, Suliman; Syied, Abdallah Abdelhameed

doi:10.1155/2021/6188097

Cited by 5 publications

References 14 publications

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Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

Syied,

De,

Bin Turki

et al. 2024

Anal.Math.Phys.

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We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field $$B_{i}$$ B i is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field $$A_{i}$$ A i is irrotational. We identify the conditions to ensure both $$B_{i}$$ B i and $$A_{i}$$ A i of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by $$p=\frac{4-n}{ 2n-2}\mu $$ p = 4 - n 2 n - 2 μ , whereas in a pseudo Ricci symmetric space-time, the state equation takes the form $$p=\frac{3-n}{n-1}\mu $$ p = 3 - n n - 1 μ , where p and $$\mu $$ μ are the isotropic pressure and the energy density. It is noteworthy that if $$n=4$$ n = 4 , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era.

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Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

Syied,

De,

Bin Turki

et al. 2024

Anal.Math.Phys.

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CHARACTERIZATIONS OF ALMOST PSEUDO-RICCI SYMMETRIC SPACETIMES UNDER GRAY's DECOMPOSITION

Hazra¹,

2023

Reports on Mathematical Physics

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Investigation of Pseudo-Ricci Symmetric Spacetimes in Gray’s Subspaces

Abstract: In the present paper, we focused our attention to study pseudo-Ricci symmetric spacetimes in Gray’s decomposition subspaces. It is proved that PRS n … Show more

Cited by 5 publications

References 14 publications

Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

CHARACTERIZATIONS OF ALMOST PSEUDO-RICCI SYMMETRIC SPACETIMES UNDER GRAY's DECOMPOSITION

GRAY's DECOMPOSITION AND WARPED PRODUCT OF GENERALIZED RICCI RECURRENT SPACETIMES

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