Abstract:
Over the past decade or so, detailed studies (primarily numerical) of
model problems for gravitational collapse have shown that interesting
behaviour generically arises at the threshold of black hole formation.
Here one considers single-parameter family of solutions to the coupled
Einstein/matter field equations such that by tuning the family parameter,
p, through some critical value, p*, a transition from
solutions containing no
black hole to solutions containing one is observed. For any given model,
the black hole threshold is generically characterized by specific critical
solutions, which have additional symmetry properties beyond what may be
prescribed in the specification of the model per se. In addition,
scaling laws, which, for example, relate the black hole mass to the
parameter-space distance from criticality,
p-p*,
can be measured from near-critical evolutions.
Much of the phenomenology that has been observed
in critical collapse is now reasonably well understood from the point of
view of perturbation theory, using a mathematical development that precisely
parallels that used in the standard treatment of statistical mechanical
critical phenomena.
Following a brief overview of black hole critical phenomena, I will
discuss some recent results from calculations performed by the UBC
numerical relativity group and collaborators. These include a study
of critical collapse using spherically symmetric perfect fluid models,
as well as some preliminary investigations of the effect of angular
momentum in collapse of massless scalar fields.