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

Singularities associated with an incomplete space-timeS are not uniquely defined until a boundaryB is attached to it. The resulting space-time-with-boundary, ¯S S B, will be termed a total space-time (TST).] Since an incomplete spacetime is compatible with a variety of boundaries, it follows thatS does not represent a unique universe, but instead corresponds to a family of universes, one for each of its distinct TSTs. It is shown here that the boundary attached to the Reissner-Nordström space-time for a point charge is invalid forq ²<m ². When the correct boundary is used, the resulting TST is inextendible. This implies that the Graves-Brill black hole cannot be produced by gravitational collapse. The same is true of the Kruskal-Fronsdal black hole for the point mass, and for those black holes which reduce to the latter for special values of their parameters.