A Derivation of the Kerr–Newman Metric Using Ellipsoid Coordinate Transformation

The Kerr–Newman metric describes a special rotating charged mass and is the most general solution
for the asymptotically stable “black-hole” solution in the Einstein–Maxwell equations in general
relativity. Because these are nonlinear partial differential equations, it is difficult to find an exact
analytical solution other than spherical symmetry. This study presented a new derivation of the Kerr–
Newman metric which is an extension of the authors’ previous research. Using the ellipsoid symmetry
of space-time in the Kerr metric, an ellipsoidal coordinate transformation method was performed and
the Kerr–Newman metric was more intuitively obtained. The relation with this method and Newman–
Janis algorithm was discussed.