Phases of massive scalar field collapse

TL;DR

This paper investigates the critical phenomena in the collapse of massive scalar fields, identifying two types of phase transitions and their associated critical solutions, with implications for understanding gravitational collapse in various matter models.

Contribution

It distinguishes between two phase transition types in scalar field collapse and links their critical solutions to unstable soliton stars and known massless solutions, expanding understanding of gravitational critical phenomena.

Findings

Type II transitions match massless scalar field solutions.

Type I transitions involve unstable soliton star solutions.

Results suggest unstable solutions are relevant to other matter models.

Abstract

We study critical behavior in the collapse of massive spherically symmetric scalar fields. We observe two distinct types of phase transition at the threshold of black hole formation. Type II phase transitions occur when the radial extent $(\lambda)$ of the initial pulse is less than the Compton wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that found by Choptuik in the collapse of massless scalar fields. Type I phase transitions, where the black hole formation turns on at finite mass, occur when $\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with masses $\alt 0.6 \mu^{-1}$. Our results in combination with those obtained for the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to the Einstein-matter equations may be relevant to the critical point of other matter models.