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Vaidya–Tikekar²⁰ model has been generalised to describe cold compact stars having concentric layers of different phases. We illustrate the model by considering a star whose inner core has a deconfined quark phase, enveloped by less compact baryonic constituents.

In this paper, we generalize core–envelope model of superdense star to a noncommutative spacetime and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein’s field equation in $\kappa$-deformed spacetime and use this to set up noncommutative version of core–envelope model describing superdense stars. We derive $\kappa$-deformed law of density variation, valid up to first-order approximation in deformation parameter and obtain radial and tangential pressures in $\kappa$-deformed spacetime. We also derive $\kappa$-deformed strong energy conditions and obtain a bound on the deformation parameter.

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 ($M$–$R$) 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 9km; (ii) normal neutron stars with radius between 9 to 12km and (iii) soft matter neutron stars having radius lying between 12 to 20km. 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.

In this research, core envelope model of a super dense spherically symmetric compact star is developed by considering anisotropic matter configuration. The core is represented by a linear equation of state (EOS), whereas the Van der Waals EOS is used in the envelope region. In the core and envelope of the star, all geometrical and physical factors are viable. The three regions, i.e. the core, envelope and outer space satisfy the junction conditions. The proposed model validates with the properties of Vela X-1, Her X-1 and SMC X-1. It is concluded that in the model presented, the core of the star compresses as the mass increases justifying the domination of gravitational effects on massive astronomical objects.