We investigate the condensation of KΛ0 meson along with Kβ
condensation in the neutrino trapped matter with and without hyperons.
Calculations are performed in the relativistic mean field models in which both
the baryon-baryon and (anti)kaon-baryon interactions are mediated by meson
exchange. In the neutrino trapped matter relevant to protoneutron stars, the
critical density of Kβ condensation is shifted considerably to higher
density whereas that of KΛ0 condensation is shifted slightly to higher
density with respect to that of the neutrino free case. The onset of Kβ
condensation always occurs earlier than that of KΛ0 condensation. A
significant region of maximum mass protoneutron stars is found to contain KΛ0 condensate for larger values of the antikaon potential. With the
appearance of KΛ0 condensation, there is a region of symmetric nuclear
matter in the inner core of a protoneutron star. It is found that the maximum
mass of a protoneutron star containing Kβ and KΛ0 condensate is
greater than that of the corresponding neutron star. We revisit the implication
of this scenario in the context of the metastability of protoneutron stars and
their evolution to low mass black holes.Comment: 26 pages; Revtex; 8 figures include