The total space-time of a point-mass when Λ ≠ 0, and its consequences for the Lake-Roeder black hole

Singularities associated with an incomplete space-time (S) are not well-defined until a boundary is attached to it. Moreover, each boundary (B) gives rise to a different singularity structure for S B, the resulting “total” space-time (TST). Since S is compatible with a variety of boundaries, it therefore does not represent a unique universe, but instead corresponds to a family of universes, one for each possible boundary. It is shown here that in the case of Weylʹs space-time for a point-mass with nonzero Λ, the boundary which he attached to it is invalid, and when the correct one is attached, the resulting TST is inextendible. This implies that the Lake-Roeder black hole cannot be produced by gravitational collapse.