General Mathematics, Vol. 5, No. 1 - 4, pp. 53-66, 1995
Abstract: First, a version of differential spaces is defined, which can be used to describe the singularities in General Relativity. Then this concept is applied to the most common singularities: In the Friedmann space-times, all freely falling pointlike particles can pass the final collapse and so emerge from the Big Bang. The topology of this singularity is very natural and agrees with the topology induced from the Fronsdal embedding. It is possible to glue together the Black Hole and the White Source of the maximal analytic extension of Schwarzschild space-times. In this way, some of the classical problems with this extension are solved. Finally, an example is given, where the mass of a particle is changed while passing through a singularity.
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