Changes in the global parameters of polytropic stars induced by the   appearance of the soft core
  The effect of a soft phase core appearance in the center of polytropic star is analyzed by means of linear response theory. Approximate formulae for the changes of radius, moment of inertia and mass-energy of non-rotating configuration with arbitrary adiabatic indices are presented, followed by an example evaluation of astrophysical observables. 
M. Bejger