Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories
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2024
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| author | Ahmed, Faizuddin Bouzenada, Abdelmalek |
| author_facet | Ahmed, Faizuddin Bouzenada, Abdelmalek |
| contents | In this paper, we explore a stationary BTZ space-time within the framework of modified gravity theory, specifically focusing on Ricci-inverse gravity. It is important to clarify that ``Ricci-inverse" refers to the inverse of the Ricci tensor, not the Ricci scalar. We consider a general class of this gravity theory, where the function $f$ is defined by $f(\mathcal{R}, \mathcal{A}, A^{μν}\,A_{μν})$, with $\mathcal{R}$ and $\mathcal{A}$ representing the Ricci and anti-curvature scalars, respectively and $A^{μν}$ is the anti-curvature tensor. We demonstrate that stationary BTZ space-time is a valid solution in this gravity theory, wherein the cosmological constant undergoes modifications due to the coupling constants. Moreover, we study another modified gravity theory known as $f(\mathcal{R})$-gravity and analyze the stationary BTZ space-time. Subsequently, we fully integrate the geodesic equations for BTZ space-time constructed within the Ricci-Inverse gravity, expressing the solutions in terms of elementary functions and compared with the GR result. We classify different types of geodesics, including null and time-like geodesics, under three conditions: (i) nonzero mass and angular momentum, $M \neq 0, J\neq 0$, (ii) massless BTZ space-time, $M=0$ and $J=0$, and (iii) $M=-1, J=0$, that is $AdS_3$-type, and analyze the results in modified gravity theories and compare with the general relativity case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories Ahmed, Faizuddin Bouzenada, Abdelmalek General Relativity and Quantum Cosmology High Energy Physics - Theory In this paper, we explore a stationary BTZ space-time within the framework of modified gravity theory, specifically focusing on Ricci-inverse gravity. It is important to clarify that ``Ricci-inverse" refers to the inverse of the Ricci tensor, not the Ricci scalar. We consider a general class of this gravity theory, where the function $f$ is defined by $f(\mathcal{R}, \mathcal{A}, A^{μν}\,A_{μν})$, with $\mathcal{R}$ and $\mathcal{A}$ representing the Ricci and anti-curvature scalars, respectively and $A^{μν}$ is the anti-curvature tensor. We demonstrate that stationary BTZ space-time is a valid solution in this gravity theory, wherein the cosmological constant undergoes modifications due to the coupling constants. Moreover, we study another modified gravity theory known as $f(\mathcal{R})$-gravity and analyze the stationary BTZ space-time. Subsequently, we fully integrate the geodesic equations for BTZ space-time constructed within the Ricci-Inverse gravity, expressing the solutions in terms of elementary functions and compared with the GR result. We classify different types of geodesics, including null and time-like geodesics, under three conditions: (i) nonzero mass and angular momentum, $M \neq 0, J\neq 0$, (ii) massless BTZ space-time, $M=0$ and $J=0$, and (iii) $M=-1, J=0$, that is $AdS_3$-type, and analyze the results in modified gravity theories and compare with the general relativity case. |
| title | Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.11922 |