Dynamics of critical collapse

TL;DR

This paper investigates the critical collapse of a massless scalar field in spherical symmetry through numerical and analytical methods, revealing unique spacetime features near singularities that differ from black hole cases.

Contribution

It provides the first approximate analytic expressions near the center and highlights distinctive geometric and dynamical properties of critical collapse.

Findings

Spacetime near the center is nearly conformally flat.

The dynamics are not described by the Kasner solution.

Kreschmann scalar scales as r^(-5.30).

Abstract

Critical collapse of a massless scalar field in spherical symmetry is systematically studied. We combine numerical simulations and asymptotic analysis, and synthesize critical collapse, spacetime singularities, and complex science. First set of approximate analytic expressions near the center are obtained. We observe that, near the center, the spacetime is nearly conformally flat, the dynamics is not described by the Kasner solution, and the Kreschmann scalar is proportional to r^(-5.30), where r is the areal radius. These features are significantly different from those in black hole singularities. It is speculated that the scalar field in critical collapse may be a special standing wave.