Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{μν}\,A_{μν})$ and $f(\mathcal{R})$ Modified Gravity Theories
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arXiv
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| Natura: | Preprint |
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2024
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| author | Ahmed, F. de Souza, J. C. R. Santos, A. F. |
| author_facet | Ahmed, F. de Souza, J. C. R. Santos, A. F. |
| contents | In this paper, our objective is to explore a time-machine space-time formulated in general relativity, as introduced by Li (Phys. Rev. D {\bf 59}, 084016 (1999)), within the context of modified gravity theories. We consider Ricci-inverse gravity of all Classes of models, {\it i.e.}, (i) Class-{\bf I}: $f(\mathcal{R}, \mathcal{A})=(\mathcal{R}+{κ\,\mathcal{R}^2}+β\,\mathcal{A})$, (ii) Class-{\bf II}: $f(\mathcal{R}, A^{μν}\,A_{μν})=(\mathcal{R}+{κ\,\mathcal{R}^2}+γ\,A^{μν}\,A_{μν})$ model, and (iii) Class-{\bf III}: $f(\mathcal{R}, \mathcal{A}, A^{μν}\,A_{μν})=(\mathcal{R}{κ\,\mathcal{R}^2}+β\,\mathcal{A}+δ\,\mathcal{A}^2+γ\,A^{μν}\,A_{μν})$ model, where $A^{μν}$ is the anti-curvature tensor, the reciprocal of the Ricci tensor, $R_{μν}$, $\mathcal{A}=g_{μν}\,A^{μν}$ is its scalar, and $β, κ, γ, δ$ are the coupling constants. Moreover, we consider $f(\mathcal{R})$ modified gravity theory and investigate the same time-machine space-time. In fact, we show that Li time-machine space-time serve as valid solutions both in Ricci-inverse and $f(\mathcal{R})$ modified gravity theories. Thus, both theory allows the formation of closed time-like curves analogue to general relativity, thereby representing a possible time-machine model in these gravity theories theoretically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_11513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{μν}\,A_{μν})$ and $f(\mathcal{R})$ Modified Gravity Theories Ahmed, F. de Souza, J. C. R. Santos, A. F. General Relativity and Quantum Cosmology In this paper, our objective is to explore a time-machine space-time formulated in general relativity, as introduced by Li (Phys. Rev. D {\bf 59}, 084016 (1999)), within the context of modified gravity theories. We consider Ricci-inverse gravity of all Classes of models, {\it i.e.}, (i) Class-{\bf I}: $f(\mathcal{R}, \mathcal{A})=(\mathcal{R}+{κ\,\mathcal{R}^2}+β\,\mathcal{A})$, (ii) Class-{\bf II}: $f(\mathcal{R}, A^{μν}\,A_{μν})=(\mathcal{R}+{κ\,\mathcal{R}^2}+γ\,A^{μν}\,A_{μν})$ model, and (iii) Class-{\bf III}: $f(\mathcal{R}, \mathcal{A}, A^{μν}\,A_{μν})=(\mathcal{R}{κ\,\mathcal{R}^2}+β\,\mathcal{A}+δ\,\mathcal{A}^2+γ\,A^{μν}\,A_{μν})$ model, where $A^{μν}$ is the anti-curvature tensor, the reciprocal of the Ricci tensor, $R_{μν}$, $\mathcal{A}=g_{μν}\,A^{μν}$ is its scalar, and $β, κ, γ, δ$ are the coupling constants. Moreover, we consider $f(\mathcal{R})$ modified gravity theory and investigate the same time-machine space-time. In fact, we show that Li time-machine space-time serve as valid solutions both in Ricci-inverse and $f(\mathcal{R})$ modified gravity theories. Thus, both theory allows the formation of closed time-like curves analogue to general relativity, thereby representing a possible time-machine model in these gravity theories theoretically. |
| title | Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{μν}\,A_{μν})$ and $f(\mathcal{R})$ Modified Gravity Theories |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.11513 |