Derivation and stability determination of black hole metrics

Abstract: The Schwarzschild metric and the Kerr metric describe the gravitational fields around static and rotating black holes, respectively. Here, we derive the Kerr metric in a simpler way than how it was derived originally and determine the stability of the Schwarzschild metric. The Kerr metric was derived by using the Einstein-Hilbert action as well as directly from the Einstein field equations. In order to do this, we first made an anzats with the help of the Weyl method. By using the same method as Chandrasekhar, we found that the Schwarzschild metric is stable.