We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter. Three classes of new exact solutions are found to the Einstein–Maxwell system. This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity. We can regain anisotropic and isotropic models from our general class of solutions. A physical analysis indicates that the charged solutions describe realistic compact spheres with anisotropic matter distribution. The equation of state is consistent with dark energy stars and charged quark matter distributions. The masses and central densities correspond to realistic stellar objects in the general case when anisotropy and charge are present.

Charged anisotropic matter with a linear equation of state, Classical and Quantum Gravity

In the present paper we obtain an anisotropic analogue of Durgapal-Fuloria (1985) perfect fluid solution. The methodology consists of contraction of anisotropic factor $\Delta$ by the help of both metric potentials $e^{\nu}$ and $e^{\lambda}$. Here we consider $e^{\lambda}$ same as Durgapal-Fuloria (1985) whereas $e^{\nu}$ is that given by Lake (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 stellar fluid distribution which clearly indicate validity of the model.

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Anisotropic models for compact stars

We perform a detailed physical analysis for a class of exact solutions for the Einstein–Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact solutions is performed by considering the charged anisotropic stars for the particular nonsingular exact model obtained by Maharaj, Sunzu and Ray. In performing such an analysis we regain masses obtained by previous researchers for isotropic and anisotropic matter. It is also indicated that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star.

Charged anisotropic models for quark stars

In this article we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized metric potential, namely, Buchdahl ansatz [Phys. Rev. D 116, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar and Finch-Skea. We developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that has a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$ and analyzed them in a uniform manner. As a result it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the frame work of anisotropic hypothesis, we consider analogue objects with similar mass and radii, such as LMC X-4, SMC X-1, EXO 1785-248 etc. to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P=P(\ensuremath{\rho})$, we demonstrate that equation of state (EoS) can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

Anisotropic compact stars in the Buchdahl model: A comprehensive study

In this work we have extended the Maurya-Gupta isotropic fluid solution to Einstein field equations to an aniso-tropic domain. To do so, we have employed the gravitational decoupling via the minimal geometric deformation approach. The present model is representing the strange star candidate LMC X-4. A mathematical, physical and graphical analysis, shown that the obtained model fulfills all the criteria to be an admissible solution of the Einstein field equations. Specifically, we have analyzed the regularity of the metric potentials and the effective density, radial and tangential pressures within the object, causality condition, energy conditions, equilibrium via Tolman–Oppenheimer–Volkoff equation and the stability of the model by means of the adiabatic index and the square of subliminal sound speeds.

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Generalized relativistic anisotropic compact star models by gravitational decoupling

In this paper we have studied the behavior of static spherically symmetric relativistic objects with locally anisotropic matter distribution considering the Tolman VII form for the gravitational potential $g_{rr}$
 in curvature coordinates together with the linear relation between the energy density and the radial pressure. The interior spacetime has been matched continuously to the exterior Schwarzschild geometry. We have investigated and analyzed different physical properties of the stellar model and presented graphically.

Relativistic anisotropic stellar models with Tolman VII spacetime

Over the years of the concept of local isotropy has become a too stringent condition in modeling relativistic self-gravitating objects. Taking local anisotropy into consideration, in this work, some analytical models of relativistic anisotropic charged strange stars have been developed. The Einstein–Maxwell gravitational field equations have been solved with a particular form of one of the metric potentials. The radial pressure and the energy density have been assumed to follow the usual linear equation of state of strange quark matter, the MIT bag model.

Some analytical models of anisotropic strange stars

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein–Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

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Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

This article was published in the European Physical Journal A [ © 2017, SIF, Springer-Verlag Berlin Heidelberg. ] and the definite version is available at :http://doi.org/10.1140/epja/i2017-12210-1. The Journal's website is at: https://link.springer.com/article/10.1140%2Fepja%2Fi2017-12210-1

A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars

This work presents an algorithm for modeling a static spherically symmetric compact object satisfying the Eiesland condition (Eiesland in Am Math Soc 27:213, 1925), a necessary and sufficient condition that a general centro-symmetric space shall be of the class 1. The model parameters are obtained accordingly by employing the boundary conditions to the interior solutions. The equation of state has been extracted from the solution and one found that it is almost linear. These models are free of physical and geometric singularities and satisfy the necessary physical conditions to have astrophysical significance. The central and surface densities, and pressures of some compact stars like PSR J1614-2230, Vela X-1 have been calculated from these models. Detailed analyses of these models have also been made with the help of numerical and graphical studies.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-018-5712-5.pdf

Mohammad Hassan Murad

Papers

Relativistic anisotropic stellar models with Tolman VII spacetime

Some analytical models of anisotropic strange stars

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars

Some families of relativistic anisotropic compact stellar models embedded in pseudo-Euclidean space \(E^5\): an algorithm