Search

In this work we construct a deformed embedding of the Reissner-Nordstrem (R-N) space-time within the framework of a noncommutative Riemannian geometry. We provide noncommutative corrections to the usual Riemannian expressions for the metric and curvature tensors. For the case of the metric tensor, the expression obtained possesses terms that are valid to all orders in the deformation parameter. Then we calculate the correction to the area of the event horizon of the corresponding noncommutative R-N black hole, obtaining an expression for the area of the black hole, which is correct up to fourth- order terms in the deformation parameter. 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 that is regularly used to extend gravity to the quantum level.Key words: black hole, noncommutativity, Moyal bracket, deformation, quantization.Nous construisons ici un plongement d'un espace-temps de Reissner-Nordstrem (R-N) dans le cadre d'une geometrie de Riemann non commutative. Nous donnons les corrections non commutatives aux expressions usuelles de Riemann pour la metrique et le tenseur de courbure. Pour le cas du tenseur metrique, l'expression obtenue possede des termes qui sont valides a tous les ordres du parametre de deformation. Nous calculons alors la correction de la surface de l'horizon (des evenements) du trou noir R-N non commutatif correspondant, obtenant une expression pour la surface du trou noir qui est correcte au quatrieme ordre du parametre de deformation. Finalement, nous ajoutons quelques commentaires sur l'un des invariants scalaires du second ordre du tenseur de Riemann, celui appele l'invariant de Kretschmann, une quantite regulierement utilisee afin d'etendre la gravite a un niveau quantique. [Traduit par la Redaction]Mots-cles: trou noir, non commutativite, bra-ket de Moyal, deformation, quantification., 1. IntroductionOne of the most important presumptions in general relativity is that the space, time, and gravity can be modeled as a sole entity called space-time. General relativity analyzes space-time [...]