A family of Finch and Skea relativistic stars

TL;DR

This paper derives new exact solutions for anisotropic charged relativistic stars within the Finch and Skea spacetime, demonstrating their physical viability and encompassing previous models as special cases.

Contribution

It introduces a family of exact solutions to Einstein-Maxwell equations for anisotropic charged stars, expanding the set of physically acceptable models with elementary and special functions.

Findings

Solutions are expressed in elementary, Bessel, and modified Bessel functions.

Models include uncharged and previously known charged solutions as special cases.

Graphical analysis confirms physical reasonableness of matter and electric profiles.

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.