Abstract
Effects of neutrino trapping on K and $\overline{K}$ production and $\overline{K}$ condensation in supernova matter are studied in the density-dependent relativistic hadron field theory and in the nonlinear $\ensuremath{\sigma}\ensuremath{-}\ensuremath{\omega}$ model with the parameter set Tm1. Our results show that critical densities for $\overline{K}$ condensation with neutrino trapping are shifted to higher densities compared with those of neutrino free. Threshold energies for K and $\overline{K}$ production are not sensitive to the effects induced by neutrino trapping. Meanwhile, it is shown that the effects of neutrino trapping decrease the maximum masses of protoneutron stars.
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