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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.16886 |
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| _version_ | 1866913771234000896 |
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| author | Larbi, Mohamed Aimen Zaim, Slimane Touati, Abdellah |
| author_facet | Larbi, Mohamed Aimen Zaim, Slimane Touati, Abdellah |
| contents | In this work, we derive non-commutative corrections to the Schwarzschild-Anti-de Sitter solution up to the first and second orders of the non-commutative parameter $Θ$. Additionally, we obtain the corresponding deformed effective potentials and the non-commutative geodesic equations for massive particles. Through the analysis of time-like non-commutative geodesics for various values of $Θ$, we demonstrate that the circular geodesic orbits of the non-commutative Schwarzschild-Anti-de Sitter black hole exhibit greater stability compared to those of the commutative one. Furthermore, we derive corrections to the perihelion deviation angle per revolution as a function of $Θ$. By applying this result to the perihelion precession of Mercury and utilizing experimental data, we establish a new upper bound on the non-commutative parameter, estimated to be on the order of $10^{-66}\,\mathrm{m}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16886 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole Larbi, Mohamed Aimen Zaim, Slimane Touati, Abdellah General Relativity and Quantum Cosmology In this work, we derive non-commutative corrections to the Schwarzschild-Anti-de Sitter solution up to the first and second orders of the non-commutative parameter $Θ$. Additionally, we obtain the corresponding deformed effective potentials and the non-commutative geodesic equations for massive particles. Through the analysis of time-like non-commutative geodesics for various values of $Θ$, we demonstrate that the circular geodesic orbits of the non-commutative Schwarzschild-Anti-de Sitter black hole exhibit greater stability compared to those of the commutative one. Furthermore, we derive corrections to the perihelion deviation angle per revolution as a function of $Θ$. By applying this result to the perihelion precession of Mercury and utilizing experimental data, we establish a new upper bound on the non-commutative parameter, estimated to be on the order of $10^{-66}\,\mathrm{m}^2$. |
| title | Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2411.16886 |