  Although nonsingular spacetimes and those containing black holes are
qualitatively quite different, there are continuous families of configurations
that connect the two. In this paper we use self-gravitating monopole solutions
as tools for investigating the transition between these two types of
spacetimes. We show how causally distinct regions emerge as the black hole
limit is achieved, even though the measurements made by an external observer
vary continuously. We find that near-critical solutions have a naturally
defined entropy, despite the absence of a true horizon, and that this has a
clear connection with the Hawking-Bekenstein entropy. We find that certain
classes of near-critical solutions display naked black hole behavior, although
they are not truly black holes at all. Finally, we present a numerical
simulation illustrating how an incident pulse of matter can induce the
dynamical collapse of a monopole into an extremal black hole. We discuss the
implications of this process for the third law of black hole thermodynamics.
