Ernst Potential of Near-Horizon Extremal Kerr Black Holes

Abstract

Abstract One way to find the solution of black holes is through the Ernst equations that is quite simple instead of solving the Einstein equation. Solution of Ernst equations for Kerr and Kerr-Newman black holes have been achieved in the last century. The magnetized case for those black holes and their Ernst potentials can be found using Harrison transformation. Herein the Ernst potential for extremal rotating Kerr and its magnetized solution is shown. In the end, we also extend this fashion for extremal Kerr-Newman black hole.