Strength of the naked singularity in critical collapse

TL;DR

This paper investigates the gravitational strength of naked singularities formed during critical scalar field collapse, demonstrating they are physically strong and cannot be extended beyond, highlighting their significance in gravitational physics.

Contribution

The study provides a numerical analysis showing that naked singularities in critical collapse are gravitationally strong, challenging the notion of their physical triviality.

Findings

Naked singularities in critical collapse are gravitationally strong.

Jacobi volume forms vanish near the singularity.

Spacetime cannot be extended beyond the singularity.

Abstract

The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi volume forms is examined along a non-spacelike geodesic in the limit of approach to the singularity. These are seen to be vanishing, thus showing that all physical objects will be crushed to zero size near the singularity. Consequently, although the critical collapse is considered to be a fine-tuning problem, the naked singularity forming is gravitationally strong. This implies that the spacetime cannot be extended beyond the singularity, thus making the singularity genuine and physically interesting. These results imply that the nature of critical collapse may need to be examined and explored further.