Noncommutative Reissner-Nordstr{\o}m Black hole

TL;DR

This paper develops a noncommutative geometric model of Reissner-Nordström black holes, deriving corrections to classical metrics and invariants, and analyzing the effects of noncommutativity on black hole properties.

Contribution

It introduces a noncommutative deformation of Reissner-Nordström spacetime, providing explicit corrections to the metric, horizon area, and curvature invariants.

Findings

Derived noncommutative corrections to the metric and curvature tensors.

Calculated horizon area corrections up to fourth order in deformation parameter.

Discussed implications for quantum gravity via noncommutative invariants.

Abstract

A deformed embedding of the Reissner-Nordstr{\o}m spacetime is constructed within the framework of a noncommutative Riemannian geometry. We find noncommutative corrections to the usual Riemannian expressions for the metric and curvature tensors, which, in the case of the metric, are valid to all orders in the deformation parameter. We calculate the area of the event horizon of the corresponding noncommutative R-N black-hole, obtaining corrections up to fourth order in the deformation parameter for the area of the black-hole. Finally we include some comments on the noncommutative version on one of the second order scalar invariants of the Riemann tensor, the so called Kretschmann invariant, a quantity regularly used in order to extend gravity to quantum level.