On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity

Abstract

Deformed Reissner-Nordström, as well as Reissner-Nordström de Sitter, solutions are obtained in a noncommutative gauge theory of gravitation. The gauge potentials (tetrad fields) and the components of deformed metric are calculated to second order in the noncommutativity parameter. The solutions reduce to the deformed Schwarzschild ones when the electric charge of the gravitational source and the cosmological constant vanish. Corrections to the thermodynamical quantities of the corresponding black holes and to the radii of different horizons have been determined. All the independent invariants, such as the Ricci scalar and the so-called Kretschmann scalar, have the same singularity structure as the ones of the usual undeformed case and no smearing of singularities occurs. The possibility of such a smearing is discussed. In the noncommutative case we have a local disturbance of the geometry around the source, although asymptotically at large distances it becomes flat.

Relativistic spectrum of hydrogen atom in the space-time non-commutativity

“…We work in spherical coordinates and make the choice 0r r r    (it is identical to that made in [12] and [13]), so we get: …”

Topics in Noncommutative Geometry Inspired Physics

“…However, this has been shown to have important phenomenological consequences [124] where NC generalization of the Schwarzschild solution has been worked out. Later on the impact of the NC effect on Charged black hole has been analyzed [213,214]. Below we will review the results of [213] where the deformed Reissner-Nordstrom solutions are given.…”

The noncommutative BTZ black hole in polar coordinates

“…In the four dimensional case, noncommutative solutions were obtained using the Poincaré gauge theory approach [5] in [18] for Schwarzschild black hole case, and in [19,20] for charged black hole case.…”