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

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

12 pages, 6 figures

References in corpus (18)

• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• The Milky Way's circular velocity curve between 4 and 14 kpc from APOGEE data
• A Periodic Table for Black Hole Orbits
• Circular motion of neutral test particles in Reissner-Nordström spacetime
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: analytical solutions
• Equatorial circular orbits in the Kerr-de Sitter spacetimes
• Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
• Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
• Orbital precession due to central-force perturbations
• Constraining non-commutative space-time from GW150914
• Light-bending in Schwarzschild-de-Sitter: projective geometry of the optical metric
• Geodesic equation in non-commutative gauge theory of gravity
• Thermodynamic Properties of Schwarzschild Black Hole in Non-Commutative Gauge Theory of Gravity
• Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity
• String Theory, Space-Time Non-Commutativity and Structure Formation
• Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity