Dynamics of critical collapse

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.