  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.
