  This work is devoted to a mathematical analysis of the distributional
Schwarzschild geometry. The Schwarzschild solution is extended to include the
singularity; the energy momentum tensor becomes a delta-distribution supported
at r=0. Using generalized distributional geometry in the sense of Colombeau's
(special) construction the nonlinearities are treated in a mathematically
rigorous way. Moreover, generalized function techniques are used as a tool to
give a unified discussion of various approaches taken in the literature so far;
in particular we comment on geometrical issues.
