Noncommutative corrections to the Schwarzschild-AdS metric shift circular orbits and yield a Mercury perihelion constraint on the noncommutative length scale near 10^-32 meters.
Geodesic Structure of the Noncommutative Schwarzschild Anti-de Sitter Black Hole I: Timelike Geodesics
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abstract
By considering particles as smeared objects, we investigate the effects of space noncommutativity on the geodesic structure in Schwarzschild-AdS spacetime. By means of a detailed analysis of the corresponding effective potentials for particles, we find the possible motions which are allowed by the energy levels. Radial and non-radial trajectories are treated and the effects of space noncommutativity on the value of the precession of the perihelion are estimated. We show that the geodesic structure of this black hole presents new types of motion not allowed by the Schwarzschild spacetime.
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Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole
Noncommutative corrections to the Schwarzschild-AdS metric shift circular orbits and yield a Mercury perihelion constraint on the noncommutative length scale near 10^-32 meters.