Critical gravitational collapse of a massive complex scalar field

TL;DR

This paper investigates the critical gravitational collapse of a massive complex scalar field, revealing type I and II behaviors, with critical solutions resembling unstable boson stars, and provides specific critical exponents and echoing periods.

Contribution

It demonstrates the existence of both type I and II critical collapse in a massive complex scalar field and identifies the critical solutions as unstable boson stars.

Findings

Type II collapse with critical exponent γ=0.38 and echoing period Δ=3.4 for small Gaussian width

Type I collapse occurs for larger Gaussian width, with solutions resembling unstable boson stars

Critical solutions match the properties and Lyapunov exponents of unstable boson stars

Abstract

We study the critical collapse of a massive complex scalar field coupled minimally to gravity. Taking as initial data a simple gaussian pulse with a shape similar to the harmonic ansatz for boson stars, we obtain critical collapse of type type I and II when varying the gaussian width $\sigma$. For $\sigma \leq 0.5$ we find collapse of type II with a critical exponent $\gamma=0.38\pm0.01$ and an echoing period $\Delta=3.4\pm0.1$. These values are very similar to the known results for a real massless scalar field. On the other hand, for $\sigma \geq 2.5$ we obtain collapse of type I. In this case we find that the critical solutions turn out to be an unstable boson stars in the ground state: all the data obtained from our simulations can be contrasted with the characteristic values for unstable boson stars and their corresponding Lyapunov exponents.