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On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
Deformed Reissner-Nordstr\"om, as well as Reissner-Nordstr\"om 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.Comment: Based on a talk given at the International Conference on Fundamental
and Applied Research in Physics "Farphys 2007", 25-28 October 2007, Iasi,
Romani