Effect of Shear viscosity on the nucleation of antikaon condensed matter in neutron stars

We investigate a first-order phase transition from hadronic matter to antikaon condensed matter during the cooling stage of protoneutron stars. The phase transition proceeds through the thermal nucleation of antikaon condensed matter. In this connection we study the effect of shear viscosity on the thermal nucleation rate of droplets of antikaon condensed matter. Here we adopt the same equation of state for the calculation of shear viscosity and thermal nucleation time. We compute the shear viscosity of neutron star matter composed of neutrons, protons, electrons and muons using the relativistic mean field model. The prefactor in the nucleation rate which includes the shear viscosity, is enhanced by several orders of magnitude compared with the $T^4$ approximation of earlier calculations. Consequently the thermal nucleation time in the $T^4$ approximation overestimates our result. Further the thermal nucleation of an antikaon droplet might be possible in our case for surface tension smaller than 20 MeV fm$^{-2}$.