Global versus Local Aspects of Critical Collapse

Abstract

This thesis deals with critical collapse of a massless scalar field coupled to Einstein's equations in spherical symmetry. The system is numerically investigated from both global and local points of view using a characteristic slicing and radial compactification. We find that the critical exponent that characterizes the discretely self-similar solution can be extracted both locally, in the self-similar region and globally, e.g. from the news function. In this sense, self-similarity is observable from future null infinity. For subcritical evolutions we have numerically analyzed the exponents of power-law tails and have found agreement with analytical calculations for radiation along null infinity and along timelike lines. We argue that for astrophysical observers the relevant falloff rate is that of future null infinity. We have also investigated the behavior of quasinormal modes (QNM) in near-critical evolutions. Although the perturbation theory underlying QNMs requires a fixed black hole background, we have found a surprising correlation between the radiation signal with the period of the first QNM determined by the time-dependent Bondi mass. In this context, we have also been able to verify a stationarity criterion based on QNMs for the Vaidya metric, which models the time-dependent Schwarzschild background.