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

In this work, we derive non-commutative corrections to the Schwarzschild-Anti-de Sitter solution up to the first and second orders of the noncommutative 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 noncommutative geodesics for various values of Θ , we demonstrate that the circular geodesic orbits of the noncommutative 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 noncommutative parameter, estimated to be on the order of 1 0 − 6 6 m 2 . [ABSTRACT FROM AUTHOR]