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We generate a general frame work to solve the Einstein system with an equation of state that describe static spherically symmetric anisotropic matter distribution in terms of a generating function. It is examined for a Van der Waals type equation of state with a physically reasonable form of generating function. The model satisfies all the required major physical properties of a realistic star. It is shown to be stable in the low-density regime that may represent a liquid–gas mixed fluid sphere.

We study static spherically symmetric space-time to describe relativistic compact objects with anisotropic matter distribution and derive two classes of exact models to the Einstein–Maxwell system with a modified Van der Waals equation of state. We motivate a Van der Waals-type equation of state to physically signify a high-density domain of quark matter, and the generated exact solutions are shown to contain several classes of exact models reported previously that correspond to various physical scenarios. Geometrical analysis shows that the physical quantities are well behaved so that these models may be used to describe anisotropic charged compact spheres.

We report a general solution in one of the gravitational potentials to the Einstein system in static spherically symmetric spacetime, modeling anisotropic strange quark matter by imposing a linear barotropic equation of state. The model generated by choosing Tolmann IV form for the gravitational potential is shown to contain the previously known anisotropic dark energy star model of Lobo (Class. Quantum Gravity 23:1525, 2006) and isotropic models of de Sitter and Einstein. Moreover, the model is shown to be physically admissible and corroborate with experimental observations on strange star candidates such as SAX J1808.4-3658 and 4U 1820-30.

We formulate a system of field equations with Van der Waals type equation of state to the Einstein field equations in spherically symmetric static spacetime to describe anisotropic compact matter and obtain a new class of solution by choosing one of the gravitational potentials. The generated model is shown to be physically admissible by satisfying the major physical conditions such as regularity of gravitational potential at the origin, positive definiteness of energy density and the radial pressure at the origin, vanishing of radial pressure at some finite radius, and monotonic decrease of the energy density and the radial pressure with increasing radius. The model also satisfy the casuality condition and match smoothly with the Schwarzschild exterior line element at the stellar boundary. We believe that the solution found through this work may assist more detailed studies of relativistic compact stellar bodies at the extremes of densities.

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

We study static spherically symmetric spacetime to describe compact objects with anisotropic matter distribution. We express the system of Einstein field equations as a new system of differential equations using a coordinate transformation, and then write the system in another form with polytropic equation of state and obtain two classes of exact models. The models satisfy all major physical features expected in a realistic star. For polytropic index n = 2, we obtain expressions for mass and density which are comparable with the reported experimental observations.

We report a general approach to solve an Einstein-Maxwell system to describe a static spherically symmetric anisotropic strange matter distribution with linear equation of state in terms of two generating functions. It is examined by choosing Tolmann IV type potential for one of the gravitational potentials and a physically reasonable choice for the electric field. Hence, the generated model satisfies all the required major physical properties of a realistic star. The effect of electric charge on physical properties is highlighted.

We establish a systematic algorithmic approach that generates new classes of solutions to the EinsteinMaxwell system in static spherically symmetric spacetime from well known uncharged solutions. A particular case is shown to satisfy all major physical features of a realistic charged star including the standard point-wise energy conditions of normal matter. The solution matches smoothly with the exterior Reissner-Nordstr¨om metric at the pressure free interface. The study, which is reported for a particular choice of gravitational potential, encourages similar approaches to study electrification of well known physically realistic uncharged models.