The Total Space-Time of a Point-Mass When the Cosmological Constant is Nonzero and Its Consequences for the Lake-Roeder Black Hole

Abstract

Singularities associated with an incomplete space-time (S) are not well-defined until a boundary is attached to it. Moreover, each boundary gives rise to a different singularity structure for 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 that in the case of Weyl's space-time for a point-mass with nonzero cosmological constant, the boundary which he attached 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.