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

TL;DR

This paper derives noncommutative deformed black hole solutions, including Reissner-Nordström and de Sitter types, analyzing their geometric, thermodynamic, and singularity properties within a gauge theory of gravity.

Contribution

It presents new noncommutative black hole solutions with second-order corrections and examines their physical and geometric properties, including singularity structure and thermodynamics.

Findings

Solutions reduce to known deformed Schwarzschild case when charge and cosmological constant vanish.

No smearing of singularities occurs in the noncommutative solutions.

Thermodynamical quantities and horizon radii are corrected by noncommutative effects.

Abstract

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.