  We present simulations of the evolution of a proto-neutron star in which
kaon-condensed matter might exist, including the effects of finite temperature
and trapped neutrinos. The phase transition from pure nucleonic matter to the
kaon condensate phase is described using Gibbs' rules for phase equilibrium,
which permit the existence of a mixed phase. A general property of neutron
stars containing kaon condensates, as well as other forms of strangeness, is
that the maximum mass for cold, neutrino-free matter can be less than the
maximum mass for matter containing trapped neutrinos or which has a finite
entropy. A proto-neutron star formed with a baryon mass exceeding that of the
maximum mass of cold, neutrino-free matter is therefore metastable, that is, it
will collapse to a black hole at some time during the Kelvin-Helmholtz cooling
stage.
  The effects of kaon condensation on metastable stars are dramatic. In these
cases, the neutrino signal from a hypothetical galactic supernova (distance
$\sim8.5$ kpc) will stop suddenly, generally at a level above the background in
the SuperK and SNO detectors, which have low energy thresholds and backgrounds.
This is in contrast to the case of a stable star, for which the signal
exponentially decays, eventually disappearing into the background. We find the
lifetimes of kaon-condensed metastable stars to be restricted to the range
40--70 s and weakly dependent on the proto-neutron star mass, in sharp contrast
to the significantly larger mass dependence and range (1--100 s) of
hyperon-rich metastable stars.
