Anisotropic compact stars in the Buchdahl model: A comprehensive study

Abstract

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.

Anisotropic generalization of isotropic models via hypergeometric equation

“…Figures 13 and 14 illustrate that the energy momentum tensor of all radii obey the condition (ix). Hence for the model parameters chosen the solution comply with requirements (i)-(ix) of a realistic star and in corroboration with reported physical quantities determined by experimental observation on strange star candidates RXJ 1856-37, Her X-1, SAX J1808.4-3658, SMC X-1 and Cen X-3 [52][53][54].…”

Core-envelope model of super dense star with distinct equation of states

“…For a physically stable configuration, the core and envelope of the stars should satisfy the following inequalities simultaneously (which are known as energy conditions [29]): (i) null energy condition ρ + p r ≥ 0 (NEC) (ii) weak energy conditions ρ + p r ≥ 0, ρ ≥ 0 (WEC r ) and ρ + p t ≥ 0, ρ ≥ 0 Fig. 12, it is clearly visible that the variation of energy conditions with r of the core and the envelope of both the stars are continuous at the interface and satisfying realistic conditions.…”

“…In their solution, apart from the continuity of metric potentials, pressure, one more physical parameter, i.e., energy density was continuous at the junction. In recent past, many attempts have been made by various authors to find exact analytic solutions of the Einstein field system using linear EOS with MIT bag model [25][26][27][28][29][30][31] as well as quadratic EOS [32][33][34][35][36][37][38][39]. On the other hand, various authors [40][41][42][43][44][45] have also explored new solutions of the Einstein field equations for anisotropic fluid under the Karmarkar condition [46].…”

A completely deformed anisotropic class one solution for charged compact star: a gravitational decoupling approach

“…Before proceeding to the next section we will mention some important comments here: (a) Initially we will solve the field Eqs. (33)- (35) via embedding class one condition to obtain a new solution for the anisotropic star. (b) Then we will solve of Maxwell Eqs.…”

“…Recently, Maurya et al [24][25][26][27][28][29] have discovered several charged and uncharged solution for the compact stars. The effect and role of anisotropy with and without equation of state (EOS) were proposed by Harko and Mak [30], Maurya et al [31][32][33][34][35], Varela et al [36]. On the other hand, Sharma and Maharaj [37] have obtained an analytical extended solution by taking a specific choice of mass function.…”