A family of Finch and Skea relativistic stars

Abstract

Several new families of exact solution to the Einstein-Maxwell system of differential equations are found for anisotropic charged matter. The spacetime geometry is that of Finch and Skea which satisfies all criteria for physical acceptability. The exact solutions can be expressed in terms of elementary functions, Bessel functions and modified Bessel functions. When a parameter is restricted to be an integer then the special functions reduce to simple elementary functions. The uncharged model of Finch and Skea (Class. Quantum Grav. 6, 467 (1989)) and the charged model of Hansraj and Maharaj (Int. J. Mod. Phys. D 8, 1311 (2006)) are regained as special cases. The solutions found admit a barotropic equation of state. A graphical analysis indicates that the matter and electric quantities are well behaved.Comment: 27 pages, submitted for publicatio

Anisotropic extension of Finch and Skea stellar model

“…• It is worthwhile to note that our class of solutions is similar to the family of solutions obtained by Maharaj et al (2016) even though the methods adopted are different. Maharaj et al (2016) have generated solutions to the master differential equation in terms of the Bessel functions which have later been expressed in closed forms for some specific range of model parameters defining the electromagnetic field and anisotropy.…”

“…Maharaj et al (2016) have generated solutions to the master differential equation in terms of the Bessel functions which have later been expressed in closed forms for some specific range of model parameters defining the electromagnetic field and anisotropy. In our work, we have utilized the Frobenius method to solve the master differential equation and showed that similar class of solutions could be obtained by terminating the series solution for a specific range of anisotropy.…”

“…Recently, by making use of the Finch-Skea ansatz, Maharaj et al (2016) have developed new families of exact solutions for an anisotropic charged matter distribution and showed that the masses and radii obtained for the class of solutions are consistent with observational data (Kileba et al (2017)). In this approach, by specifying the metric function g rr , the system is solved for the other metric function g tt in terms of the Bessel functions which eventually gets transformed to simple trigonometric/algebraic forms for a specific range of parameter values.…”

“…This is so because, in our work, we have assumed x = r 2 /R 2 and Z = 1/(1 + x) whereas in the formulation of Maharaj et al (2016) the following assumptions were made: x = Cr 2 , Z = 1/(1 + ax). We must point out here that in the studies of Maharaj et al (2016), a large family of exact solutions to the master equation in terms of elementary functions, Bessel functions and modified Bessel functions have been generated. It has also been illustrated with several examples that it is possible to express the solutions in terms of elementary functions and special functions by suitably fixing the model parameters.…”

Relativistic stars with conformal symmetry

“…Linear relationships involving radial pressure and the energy density exist in anisotropic stellar models of Mafa Takisa et al [20], Sunzu et al [21,22] and Kileba Matondo and Maharaj [23]. Recently, a new approach with anisotropic pressure has been investigated with the Finch and Skea geometry by Maharaj et al [24] and Kileba Matondo et al [25].…”