Material and electromagnetic sources of the Kerr-Newman geometry

Abstract

A method based on the theory of distributions, introduced by the author to analyse Kerr's singularity, is extended to the study of the Kerr-Newman geometry. In this case both the metric tensor and the electromagnetic potential are considered to be distributions defined all over space-time. The second partial derivatives of these quantities, when inserted into the coupled Einstein-Maxwell equations, give distributions with support on the singular ring and equatorial disk. By this means the sources of Kerr-Newman's geometry are determined. They are consistent with a model of a charged material disk made out of a mixture of two surface fluids, gas and dust, rigidly rotating with angular velocity ω=a−1. It is also verified that the material stress-energy tensor, as well as the electromagnetic-current vector, correctly reproduces the known asymptotic values of mass, charge and angular momentum of the collapsed object, provided due account is taken of the energy and angular momentum lying outside the source. Furthermore, a mapping of the electromagnetic field in the vicinity of the singularity is achieved by drawing the electric and magnetic lines of force. A close examination of the boundary conditions obeyed by these lines of force points to the conclusion that the massive equatorial disk is, in fact, a superconductor.