An exploration of the curvature and inheritance properties of the Interior black hole spacetime
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909596586606592 |
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| author | Shaikh, Absos Ali Kamiruzzaman |
| author_facet | Shaikh, Absos Ali Kamiruzzaman |
| contents | In continuation of the study in \cite{SDHK_interior_2020}, the present article explores the geometric and curvature properties of the interior black hole (briefly, IBH) spacetime. It is shown that in an IBH spacetime the operator $R\cdot C$ and $C\cdot R$ does not commute with each other and infact the commutator $C\cdot R-R\cdot C$ is linearly dependent with $Q(g,R)$ and $Q(S,R)$ as well as $Q(g,C)$ and $Q(S,C)$. Also in IBH spacetime $R \cdot R$ is linearly dependent with $Q(S,R)$ and $Q(g,C)$. It is exhibited that IBH spacetime is $2$-quasi Einstein, Ein$(2)$ and generalized quasi Einstein spacetime in the sense of Chaki, and its conformal $2$-forms are recurrent. We have derived the universal form of the compatible tensors in such a spacetime. We have also demonstrated that the nature of energy momentum tensor of IBH spacetime is pseudosymmetric (see, Theorem $4.1$). Again it is exposed that with respect to the non-Killing vector field $\frac{\partial}{\partial t},$ the IBH spacetime obeys the generalized curvature inheritance, generalized Ricci inheritance, special type of generalized conformal, concircular, conharmonic and generalized Weyl projective inheritance. Finally a comparison between IBH spacetime and KIselev Black Hole (KBH) is displayed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_20060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exploration of the curvature and inheritance properties of the Interior black hole spacetime Shaikh, Absos Ali Kamiruzzaman General Physics 53B20, 53B30, 53B50, 53C15, 53C25, 53C35, 83C15 In continuation of the study in \cite{SDHK_interior_2020}, the present article explores the geometric and curvature properties of the interior black hole (briefly, IBH) spacetime. It is shown that in an IBH spacetime the operator $R\cdot C$ and $C\cdot R$ does not commute with each other and infact the commutator $C\cdot R-R\cdot C$ is linearly dependent with $Q(g,R)$ and $Q(S,R)$ as well as $Q(g,C)$ and $Q(S,C)$. Also in IBH spacetime $R \cdot R$ is linearly dependent with $Q(S,R)$ and $Q(g,C)$. It is exhibited that IBH spacetime is $2$-quasi Einstein, Ein$(2)$ and generalized quasi Einstein spacetime in the sense of Chaki, and its conformal $2$-forms are recurrent. We have derived the universal form of the compatible tensors in such a spacetime. We have also demonstrated that the nature of energy momentum tensor of IBH spacetime is pseudosymmetric (see, Theorem $4.1$). Again it is exposed that with respect to the non-Killing vector field $\frac{\partial}{\partial t},$ the IBH spacetime obeys the generalized curvature inheritance, generalized Ricci inheritance, special type of generalized conformal, concircular, conharmonic and generalized Weyl projective inheritance. Finally a comparison between IBH spacetime and KIselev Black Hole (KBH) is displayed. |
| title | An exploration of the curvature and inheritance properties of the Interior black hole spacetime |
| topic | General Physics 53B20, 53B30, 53B50, 53C15, 53C25, 53C35, 83C15 |
| url | https://arxiv.org/abs/2504.20060 |