New possible quark-hadron mixed phase in protoneutron stars.

The transition from hadronic to quark matter at high density is a strong first order phase transition if the surface tension between the two phases is large. While this implies a constant-pressure mixed phase in cold neutron star matter this is not the case for the hot and lepton rich matter of protoneutron stars. By considering the global conservation of lepton number during the stage of neutrino trapping, we show that a new mixed phase with non-constant pressure could appear in protoneutron stars and it would gradually disappear during deleptonization. We discuss the peculiar properties of this mixed phase and its possible significant effects on the evolution of protoneutron stars and their neutrino emission.