We have computed the properties of compact objects like neutron stars based on equation of state (EOS) deduced from a core–envelope model of superdense stars. Such superdense stars have been studied by solving Einstein’s equation based on pseudo-spheroidal and spherically symmetric spacetime geometry. The computed star properties are compared with those obtained based on nuclear matter EOSs. From the mass–radius ([Formula: see text]–[Formula: see text]) relationship obtained here, we are able to classify compact stars in three categories: (i) highly compact self-bound stars that represents exotic matter compositions with radius lying below 9[Formula: see text]km; (ii) normal neutron stars with radius between 9 to 12[Formula: see text]km and (iii) soft matter neutron stars having radius lying between 12 to 20[Formula: see text]km. Other properties such as Keplerian frequency, surface gravity and surface gravitational redshift are also computed for all the three types. This work would be useful for the study of highly compact neutron like stars having exotic matter compositions.

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