The naked singularity in the global structure of critical collapse spacetimes

TL;DR

This paper investigates the global structure of critical scalar field collapse spacetimes, revealing a naked singularity and addressing paradoxes in their Penrose diagrams through numerical and theoretical analysis.

Contribution

It demonstrates that the limiting spacetime in critical collapse has a naked singularity and clarifies the nature of the Penrose diagram differences via gauge transformations.

Findings

Limiting spacetime converges pointwise for all r>0

The r=0 line differs in the limits, indicating a discontinuity

The spacetime contains a naked singularity that is future removable

Abstract

We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity.