The Total Space-Time of a Point Charge and Its Consequences for Black Holes

TL;DR

This paper explores the concept of total space-times for point charges and demonstrates that certain black hole solutions cannot be formed by gravitational collapse when proper boundaries are considered, impacting black hole formation theories.

Contribution

It introduces the concept of total space-times (TST) for point charges and shows that proper boundary choices make some classical black hole solutions inextendible, challenging their physical formation.

Findings

The boundary for Reissner-Nordstrom space-time with q^2 < m^2 is invalid.

Proper boundary choice makes the TST inextendible.

Graves-Brill and Kruskal-Fronsdal black holes cannot form via gravitational collapse.

Abstract

Singularities associated with an incomplete space-time (S) are not uniquely defined until a boundary is attached to it. [The resulting space-time-with-boundary will be termed a "total" space-time (TST).] Since an incomplete space-time is compatible with a variety of boundaries, it follows that S does not represent a unique universe but instead corresponds to a family of universes, one for each of the distinct TSTs. It is shown here that the boundary attached to the Reissner-Nordstrom space-time for a point charge is invalid for q^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.