We have proposed a model for relativistic compact star with anisotropy and analytically obtained exact spherically symmetric solutions describing the interior of the dense star admitting non-static conformal symmetry. Several features of the solutions including drawbacks of the model have been explored and discussed. For this purpose we have provided the energy conditions, TOV-equations and other physical requirements and thus thoroughly investigated stability, mass-radius relation and surface redshift of the model. It is observed that most of the features are well matched with the compact stars, like quark/strange stars.

In the current article, we study anisotropic spherically symmetric strange star under the background of f (R, T ) gravity using the metric potentials of Tolman-Kuchowicz type [1,2] as λ(r) = ln(1 + ar 2 + br 4 ) and ν(r) = Br 2 + 2 ln C which are free from singularity, satisfy stability criteria and also well behaved. We calculate the value of constants a, b, B and C using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) where the density profile (ρ) is related to the radial pressure (p r ) as p r (r) = 1 3 (ρ − 4B g ). Here quark pressure is responsible for generation of bag constant B g . Motivation behind this study lies in finding out a nonsingular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herrera's cracking condition and also with Harrison-Zel ′ dovich-Novikov's static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model.

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We investigate perfect fluid stars in (2 + 1) dimension in pseudo-spheroidal spacetime with the help of Vaidya-Tikekar metric where the physical 3-space (t = constant) is described by pseudo-spheroidal geometry. Here the spheroidicity parameter a, plays an important role for determining the properties of a compact star. In the present work a class of interior solutions corresponding to the Bañados-Teitelboim-Zanelli (BT Z) (Baados et al., Phys. Rev. Lett. 69:1849Lett. 69: , 1992 exterior metric has been provided which describes a static circularly symmetric star with negative cosmological constant in equilibrium. It is shown that asymptotically anti-de Sitter (2 + 1) dimensional spacetime described by BTZ admits a compact star solution with reasonable physical features.