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

TL;DR

This paper examines the structure of space-time around a point-mass with a nonzero cosmological constant, revealing that the Lake-Roeder black hole cannot form through gravitational collapse due to boundary issues.

Contribution

It demonstrates that the boundary used in Weyl's space-time is invalid and that the correct boundary makes the total space-time inextendible, challenging previous black hole formation models.

Findings

Weyl's boundary is invalid for nonzero cosmological constant

Correct boundary makes the total space-time inextendible

Lake-Roeder black hole cannot result from gravitational collapse

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.