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arXiv · 2411.16886

Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole

Mohamed Aimen Larbi·Slimane Zaim·Abdellah Touati
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Abstract

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 $\Theta$. 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 $\Theta$, 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 $\Theta$. 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 $10^{-66}\,\mathrm{m}^2$.

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Mohamed Aimen Larbi, Slimane Zaim, Abdellah Touati. 2024-11-25. Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole. https://doi.org/10.1142/s0217732325500609

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