Derivation of the Metric of Reissner-Nordström and Kerr-Newman Black Holes

Abstract

In this thesis, both the geometrical and action principle approach to Einstein’s field equations are developed, providing an intuitive fundamental path also with a more formal development given by an extremal principle. After this solid introduction, derivations of the metric of two distinct theoretical models of black holes are presented. Firstly, the Reissner-Nordstrom model is studied and its metric is obtained by solving the differential ¨ field equations. Secondly, the Kerr-Newman model is approached by the Newman-Jannis algorithm that provides an easy and straightaway procedure to obtain its metric and energymomentum tensor just by identifying a seed metric and applying a change of variables. Finally, the solutions are studied, horizons and regions of interest of both black holes are commented.