Distributional energy--momentum tensor of the Kerr--Newman spacetime family

Abstract

Using the Kerr-Schild decomposition of the metric tensor that employs the algebraically special nature of the Kerr-Newman space-time family, w e calculate the energy-momentum tensor. The latter turns out to be a wellde ned tensor-distribution with disk-like support.

Classical, geometric origin of magnetic moments, spin-angular momentum, and the Dirac gyromagnetic ratio

“…What we are calling the charge, the dipole moments, the mass and angular momentum are the coefficients of the relevant terms in r −1 expansions of the Maxwell and gravitational fields. The structure of the sources has been discussed elsewhere 2,3,4,5,6 .…”

The use of generalized functions and distributions in general relativity

“…Balasin and Nachbagauer considered rotating, charged, Kerr-Newman black-hole solutions in a number of papers ( [4,5,6,7,9,10]). The solutions considered have the feature that they are all examples of Kerr-Schild geometries.…”

Remarks on the distributional Schwarzschild geometry

“…Eventually, its distributional limit is computed and-via the field equations-a distributional energy momentum tensor is obtained. This tensor may then be interpreted as distributional source of the Schwarzschild geometry [9,10,11,12,13]. However, using ad-hoc regularizations we are confronted with the problem of regularization independence of the results which may not be suitably addressed within this setting.…”

“…Hence, we are going to take another more geometrical view-point in this section. The main idea-following [10,20]-is to use the Kerr-Schild form of the Schwarzschild metric. Retaining this preferred structure also during the whole regularization process will enable us to derive the physically desired result in a rigorous manner.…”