Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909230048477184 |
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| author | De, Uday Chand De, Krishnendu |
| author_facet | De, Uday Chand De, Krishnendu |
| contents | In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime and a pseudo generalized Ricci-recurrent perfect fluid spacetime represents either a dark energy epoch of the Universe or, the velocity vector field is parallel, conservative, acceleration-free, vorticity-free, and shear-free and becomes a static spacetime. Lastly, we study the impact of this spacetime under $f(\mathcal{R})$ gravity scenario and deduce several energy conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity De, Uday Chand De, Krishnendu General Relativity and Quantum Cosmology Differential Geometry In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime and a pseudo generalized Ricci-recurrent perfect fluid spacetime represents either a dark energy epoch of the Universe or, the velocity vector field is parallel, conservative, acceleration-free, vorticity-free, and shear-free and becomes a static spacetime. Lastly, we study the impact of this spacetime under $f(\mathcal{R})$ gravity scenario and deduce several energy conditions. |
| title | Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2406.16113 |