We discuss different exotic phases and components of matter from the crust tothe core of neutron stars based on theoretical models for equations of staterelevant to core collapse supernova simulations and neutron star merger.Parameters of the models are constrained from laboratory experiments. It isobserved that equations of state involving strangeness degrees of freedom suchas hyperons and Bose-Einstein condensates are compatible with 2M$_{solar}$neutron stars. The role of hyperons is explored on the evolution and stabilityof the protoneutron star (PNS) in the context of SN1987A. Moment of inertia,mass and radius which are direct probes of neutron star interior are computedand their observational consequences are discussed. We continue our study onthe dense matter under strong magnetic fields and its application tomagnetoelastic oscillations of neutron stars.
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