We select 37 most common and realistic dense matter equation of states to integrate the general relativistic stellar structure equations for static spherically symmetric matter configurations. For all these models, we check the compliance of the acceptability conditions that every stellar model should satisfy. It was found that some of the non-relativistic equation of states violate the causality and/or the dominant energy condition and that adiabatic instabilities appear in the inner crust for all equation of state considered.
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