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 solution to the spherically symmetric, static Einstein field equations(EFEs) with a perfect fluid source, including in particular the Vaidya-Tikekar and Finch-Skea. We here developed the model by considering anisotropic spherically symmetric static general relativistic configuration that plays 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 an 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 maintain 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 (ρ), we demonstrate that EoSs can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

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In this work, we explore a class of compact charged objects that have been tested against experimental and observational constraints with some known compact stars candidates. This study is performed by considering the self-gravitating, charged, isotropic fluids which are more pliability in solving the Einstein-Maxwell equations. In order to determine the interior geometry, we utilize the VaidyaTikekar (J Astrophys Astron 3:325, 1982) geometry for the metric potential with Riessner-Nordström metric as an exterior solution. These model parameters are determined after selecting some particular values of M and R, for the compact objects SAX J1808.4-3658, Her X-1 and 4U 1538-52. The most striking consequence is that hydrostatic equilibrium is maintained for different forces, and the situation is clarified by using the generalized Tolman-Oppenheimer-Volkoff equation. In addition to this, we also present the energy conditions, speeds of sound and compactness of stars that are very much compatible to that for a physically acceptable stellar model. Arising solutions are also compared with graphical representations that provide strong evidences for more realistic and viable models, both at theoretical and astrophysical scale.

This paper aims to explore a class of static stellar equilibrium configuration of relativistic charged spheres made of a charged perfect fluid. For solving the Einstein-Maxwell field equations, we consider a particularized metric potential, Buchdahl ansatz [1] and then by using a simple transformation. The study is developed by matching the interior region with Riessner-Nordström metric as an exterior solution. The matter content the charged sphere satisfies all the energy conditions and hydrostatic equilibrium equation, i.e. the modified Tolman-Oppenheimer-Volkoff (TOV) equation for the charged case is maintained. In addition to this, we also discuss some important properties of the charged sphere such as total electric charge, mass-radius relation, surface redshift, and the speed of sound. Obtained solutions are presented by the graphical representation that provides strong evidence for a more realistic and viable stellar structure. Obtained results are compared with analogue objects with similar mass and radii, such as SAX J1808.4-3658, 4U 1538-52, PSR J1903+327, Vela X-1, and 4U1608-52. It is also noted that the Buchdahl ansatz for a given transformation provides a physically viable solution only for the charged case when 0 < K < 1, where density and pressure are maximum at the center and monotonically decreasing towards the boundary. Obtained results are also quite important both from theoretical and astrophysical scale to analyze other compact objects such as white dwarfs, neutron stars, boson stars, and quark stars.