On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity
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| Format: | Preprint |
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2024
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| _version_ | 1866917763456434176 |
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| author | Suh, Young Jin De, Krishnendu De, Uday Chand |
| author_facet | Suh, Young Jin De, Krishnendu De, Uday Chand |
| contents | This article delivers the characterization of a pseudo $B$ symmetric spacetimes and we illustrate that a pseudo $B$ symmetric spacetime admitting Codazzi type of $B$-tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo $B$ symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo $B$ symmetric spacetime with Codazzi type of $B$-tensor the electric part of the Weyl tensor vanishes and has Riemann and Weyl compatible vector fields. Furthermore, it is established that the chosen spacetime with Codazzi type of $B$-tensor is conformally flat and represents a Robertson-Walker spacetime. Also, we calculate the scale factor $\varPsi (t)$ for these spacetimes in a spatially flat Robertson-Walker spacetime. Finally, we study the impact of this spacetime under $f(R)$ gravity scenario and deduce several energy conditions by considering a new model $f\left(\mathcal{R}\right)= e^{(α\mathcal{R})}-ln(β\mathcal{R})$ in which $α$ and $β$ are positive constants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity Suh, Young Jin De, Krishnendu De, Uday Chand General Relativity and Quantum Cosmology Differential Geometry This article delivers the characterization of a pseudo $B$ symmetric spacetimes and we illustrate that a pseudo $B$ symmetric spacetime admitting Codazzi type of $B$-tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo $B$ symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo $B$ symmetric spacetime with Codazzi type of $B$-tensor the electric part of the Weyl tensor vanishes and has Riemann and Weyl compatible vector fields. Furthermore, it is established that the chosen spacetime with Codazzi type of $B$-tensor is conformally flat and represents a Robertson-Walker spacetime. Also, we calculate the scale factor $\varPsi (t)$ for these spacetimes in a spatially flat Robertson-Walker spacetime. Finally, we study the impact of this spacetime under $f(R)$ gravity scenario and deduce several energy conditions by considering a new model $f\left(\mathcal{R}\right)= e^{(α\mathcal{R})}-ln(β\mathcal{R})$ in which $α$ and $β$ are positive constants. |
| title | On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2408.16976 |