The total space-time of a point charge and its consequences for black holes

Singularities associated with an incomplete space-time (S) are not uniquelydefined until a boundary is attached to it. [The resultingspace-time-with-boundary will be termed a "total" space-time (TST).] Since anincomplete space-time is compatible with a variety of boundaries, it followsthat S does not represent a unique universe but instead corresponds to a familyof universes, one for each of the distinct TSTs. It is shown here that theboundary attached to the Reissner-Nordstrom space-time for a point charge isinvalid for q^2 < m^2. When the correct boundary is used, the resulting TST isinextendible. This implies that the Graves-Brill black hole cannot be producedby gravitational collapse. The same is true of the Kruskal-Fronsdal black holefor the point mass, and for those black holes which reduce to the latter forspecial values of their parameters.