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.
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