  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.
