The infinite red-shift surfaces of the Kerr and Kerr-Newman solutions of the Einstein field equations

Abstract

In contrast to the Schwarzschild solution, the infinite red-shift surfaces and null surfaces of the Kerr solution to the axially-symmetric Einstein field equations are distinct. Some three-dimensional depictions of these surfaces are presented here for observers following the time-like Killing vector of the Kerr and Kerr-Newman solutions. Some similarities of the latter to the Reissner-Nordstrom solution are also discussed. In the case of the Kerr solution, the inner infinite red-shift surface terminates at the ring singularity. This is not the case for the Kerr-Newman solution where the infinite red-shift surface and the ring singularity have no points in common. The presence of charge severs the relation between the singularity and the infinite red-shift surface. This paper is also intended to fill a void in the literature where few, if any, adequate representations of the infinite red-shift surfaces and their relation to the singularity and horizons exist.