Speaker
Description
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions
near the threshold of black hole formation exhibit critical behavior. One aspect of this is that
threshold solutions themselves are self-similar and are, in a certain sense, unique. To an extent
yet to be fully understood, the same phenomena persist beyond spherical symmetry. It is therefore
desirable to construct simple non-linear models that exhibit such symmetry at the threshold of blow-
up. This can help understand both the structural requirements on the non-linearities and the extent
to which nearby solutions may display critical behavior. Presently, starting with deformations of
the wave equation, we discuss models which have discretely self-similar threshold solutions. We
study the behavior of threshold solutions in the past light cone of the blow-up point and show
that in spherical symmetry there is a clear sense in which a unique critical solution exists. Near
threshold spherical numerical evolutions are also presented for more general models, and exhibit
similar behavior. Uniqueness at the threshold of blow-up is, however, completely lost in general.
