We present a class of Gaussian coordinate systems for the Kerr metric obtained from the relativistic Hamilton-Jacobi equation. We discuss the Cauchy problem of such a coordinate system. In the appendix, we present the JEK (Jordan-Ehlers-Kundt) formulation of General Relativity—the so-called quasi-Maxwell equations—which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to regain the internal metric of the Schwarzschild solution and, with this in mind, we suggest a possible way to find out a physically significant internal solution for the Kerr metric.
Authors: M. Novello and E. Bittencourt.