Geodesic equation in non-commutative gauge theory of gravity*

Abstract

Abstract In this study, we construct a non-commutative gauge theory of the modified structure of the gravitational field using the Seiberg-Witten map and the general tetrad fields of Schwarzschild space-time to show that the non-commutative geometry removes the singularity at the origin of the black hole, thus obtaining a non-singular Schwarzschild black hole. The geodetic structure of this black hole presents new types of motion next to the event horizon within stable orbits that are not allowed by the ordinary Schwarzschild spacetime. The noncommutative periastron advance of the Mercury orbit is obtained, and with the available experimental data, we find a parameter of non-commutativity on the order of . This result shows that the new fundamental length, , is on the order of .