Kerr-Schild Metric Research Articles

Kerr-Schild metric cannot have an accelerating source

We give a simple proof that if the source of a vacuum electro-magnetic or purely gravitational Kerr-Schild metric is a world-line in the background Minkowski space-time then the 4-acceleration of the world-line must vanish.

A generalized Kerr-Schild solution of Einstein's equations

AbstractA very general exact solution of Einstein's equation Rik = σξiξk, is given in terms of the Kerr-Schild metric, gik = ηij + Hξiξk, where ξi is a shearfree geodetic null congruence. The Kerr-Schild solution for Rik = 0 is derived as a particular case.

Expansion-free Kerr-Schild fields

The expansion-free Kerr-Schild fields are studied starting with the general Kerr-Schild metric in a vacuum space--time. (JFP)

Einstein Spaces with Symmetry Groups

In this paper, we construct all possible groups of motion (symmetry groups) for empty Einstein spaces admitting a diverging, geodesic, and shear-free ray congruence. (Minkowski space is excluded throughout the discussion.) It is proved that any such Einstein space cannot admit a symmetry group with dimension greater than four. Although the field equations are not solved completely for spaces with groups of dimension one or two, a generalization of the Kerr spinning-mass solution is obtained from the 2-dimensional class. It is shown that all such spaces with 4-dimensional symmetry groups are well known: Schwarzschild, NUT (Newman, Unti, and Tamborino), and a particular hypersurface orthogonal Kerr-Schild metric. The only member of these spaces admitting a 3-dimensional symmetry group is a Petrov Type III hypersurface orthogonal metric.