Critical gravitational collapse of a massive complex scalar field
Erik Jiménez-Vázquez, Miguel Alcubierre
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 I and II when varying the Gaussian width $\ensuremath{\sigma}$. For $\ensuremath{\sigma}\ensuremath{\le}0.5$ we find collapse of type II with a critical exponent $\ensuremath{\gamma}=0.38\ifmmode\pm\else\textpm\fi{}0.01$ and an echoing period $\mathrm{\ensuremath{\Delta}}=3.4\ifmmode\pm\else\textpm\fi{}0.1$. These values are very similar to the well-known results for a real massless scalar field. On the other hand, for $\ensuremath{\sigma}\ensuremath{\ge}2.5$ we obtain the 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.