Differential spaces and singularities of space-time (Q2733975)

The author prepares first the foundations of geometric spaces, on which he constructs a theory of singularities of space-times. In Section 2 he gives a version of differential spaces, which he calls \(d\)-spaces. Sections 3 and 4 are devoted to singularities of the Friedmann space-time and Schwarzschild space-time, respectively. Using the theory of \(d\)-spaces, he proves that it is possible to glue the black hole to the white source in such a way that causality is conserved locally. In Section 5 the space-times with edges are discussed. The author gives an example where the mass of a particle is changed while passing through a singularity.