The implications of the formation of strange quark matter in neutron stars
and in core-collapse supernovae is discussed with special emphasis on the
possibility of having a strong first order QCD phase transition at high baryon
densities. If strange quark matter is formed in core-collapse supernovae
shortly after the bounce, it causes the launch of a second outgoing shock which
is energetic enough to lead to a explosion. A signal for the formation of
strange quark matter can be read off from the neutrino spectrum, as a second
peak in antineutrinos is released when the second shock runs over the
neutrinosphere.Comment: 10 pages, 8 figures, invited talk given at the international
conference on strangeness in quark matter (SQM2008), Beijing, October 6-10,
Beijing, China, version to appear in J. Phys.