Using distributional techniques we calculate the energy-momentum tensor of the Schwarzschild geometry. It turns out to be a well-defined tensor-distribution concentrated on the r = 0 region which is usually excluded from space-time. This provides a physical interpretation for the curvature of this geometry.

Exact stationary axially symmetric solutions of the 4-dimensional Einstein equations with co-rotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments over-estimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down in an extended rotating region, even though it is valid locally everywhere. No conflict with solar system tests arises.

The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry together with their respective energy-momentum tensors is derived. The approach is based on tensor-distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.

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.

Dedication:We feel honored to dedicate this article to Andrzej Trautman on the occasion of his 8 2 -th birthday AbstractWe generalize previous [1] work on the classification of (C ∞ ) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normalform-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.