Generalised compact spheres in electric fields

TL;DR

This paper derives exact solutions to the Einstein-Maxwell equations for spherically symmetric charged bodies, expanding the class of known models for relativistic spheres and neutron stars using advanced mathematical functions.

Contribution

It introduces a more general method for solving the Einstein-Maxwell system, encompassing previous solutions and allowing for broader classes of charged and uncharged relativistic models.

Findings

Derived new exact solutions using special and elementary functions.

Included previous models as special cases within the new solutions.

Expanded the mathematical framework for modeling charged relativistic spheres.

Abstract

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with variable, rational coefficients. In an earlier treatment this condition was integrated by first transforming it to a hypergeometric equation. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system both in the form of special functions and elementary functions. Our results contain particular solutions found previously including models of charged relativistic spheres and uncharged neutron star models.