Curvature properties of spacelike hypersurfaces in a RW spacetime

Chen, Bang-Yen; Lone, Mehraj Ahmad; Vîlcu, Alina-Daniela; Vîlcu, Gabriel-Eduard

doi:10.1016/j.geomphys.2023.105015

Journal of Geometry and Physics

2023

DOI: 10.1016/j.geomphys.2023.105015

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Curvature properties of spacelike hypersurfaces in a RW spacetime

Bang-Yen Chen,

Mehraj Ahmad Lone,

Alina-Daniela Vîlcu

et al.

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2024

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Cited by 3 publications

References 84 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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On some basic curvature invariants of screen homothetic lightlike hypersurfaces in a GRW spacetime

Harry,

Lone,

Vîlcu

et al. 2024

Differential Geometry and its Applications

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Characterization of warped product manifolds through the W2-curvature tensor with applications to relativity

Syied,

De,

Turki

et al. 2024

Heliyon

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Curvature properties of spacelike hypersurfaces in a RW spacetime

Cited by 3 publications

References 84 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

On some basic curvature invariants of screen homothetic lightlike hypersurfaces in a GRW spacetime

Characterization of warped product manifolds through the W2-curvature tensor with applications to relativity

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