The corrections to the metric of Reissner-Nordström Black Hole from the Generalized Uncertainty Principle

Abstract

The emergence of the minimal observable length is commonly accepted in most of the quantum gravitational candidates. The existence of such a minimal length in high energy physics necessitates some revisions to the standard uncertainty principle. The generalized uncertainty principle is particularly suitable for incorporating such a finite resolution of the space-time and may provide a useful phenomenological approach to study the physics of quantum gravity. It is possible to use the generalized uncertainty principle to modify the black hole thermodynamics straightforwardly. However, it is also possible to use the generalized uncertainty principle to modify the black hole metric itself. In this paper, we are going to modify the Reissner-Nordström metric in the presence of the quantum gravitational effects via the generalized uncertainty principle. Then, we use the modified charged black hole metric to study the black hole thermodynamics. The modified metric is also applied to study the light deflection angle.