In the present paper we obtain an anisotropic analog of the Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985) perfect fluid solution. The methodology consists of contraction of the anisotropic factor with the help of both metric potentials e ν and e λ . Here we consider e λ the same as Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985) did, whereas e ν is as given by Lake (Phys Rev D 67:104015, 2003). The field equations are solved by the change of dependent variable method. The solutions set mathematically thus obtained are compared with the physical properties of some of the compact stars, strange star as well as white dwarf. It is observed that all the expected physical features are available related to the stellar fluid distribution, which clearly indicates the validity of the model.

In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.

We present new anisotropic models for Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] type perfect fluid solution. For this purpose, we started with metric potential [Formula: see text] same as Buchdahl [H. A. Buchdahl, Phys. Rev. 116 (1959) 1027.] and [Formula: see text] is monotonically increasing function as suggested by Lake [K. Lake, Phys. Rev. D 67 (2003) 104015]. After that we determine the new pressure anisotropy factor [Formula: see text] with the help of both the metric potentials [Formula: see text] and [Formula: see text] and propose new well behaved general solution for anisotropic fluid distribution. The physical quantities like energy density, radial and tangential pressures, velocity of sound and redshift etc. are positive and finite inside the compact star. In this connection, we have studied the stability of the models, which is most vital one and also we determined the equation of state [Formula: see text] for the realistic compact star models. It is noted that the mass and radius of our models can represent the structure of realistic astrophysical objects such as Her X-1 and RXJ 1856-37.

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We presented a non-singular solution of Einstein’s field equations using gravitational decoupling by means of complete geometric deformation (CGD) in the anisotropic domain for compact star models. In this approach both the gravitational potentials are deformed as $$ \nu =\xi +\beta \,h(r)$$ν=ξ+βh(r) and $$ e^{-\lambda }=\mu +\beta \,f(r)$$e-λ=μ+βf(r), where $$\beta $$β is a coupling constant. Then we solve more complex field equations under above transformations by using a particular form of deformation function h(r) for two different cases namely the mimic constraint for the pressure $$\{p(r)=\theta ^1_1\}$${p(r)=θ11} and the mimic constraint for the density $$\{\rho (r)=\theta _0^0\}$${ρ(r)=θ00} (Ovalle in Phys Lett B 788:213, 2019). The compact star models have been constructed by taking $$M_0/R=0.2$$M0/R=0.2 for two different non-zero values of $$\beta $$β. Moreover, the boundary conditions are also performed for the said complete geometric deformation in the presence of anisotropic matter distribution. We also find pressure, density, anisotropy and causality conditions that are physically acceptable throughout the model. The $$M-R$$M-R curve is also presented to support our model for describing a realistic compact object such as neutron stars.