Exact models for isotropic matter

TL;DR

This paper derives explicit exact solutions to the Einstein-Maxwell equations for static, spherically symmetric charged matter distributions, generalizing previous models and providing solutions in elementary functions.

Contribution

It introduces a method to solve the pressure isotropy condition as a recurrence relation, enabling explicit solutions for the Einstein-Maxwell system in closed form.

Findings

Explicit solutions for metric functions, density, pressure, and electric field.

Models include and extend previous neutron star solutions.

Series solutions can be truncated to elementary functions.

Abstract

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series we show that the series terminate and there exist two linearly independent solutions. Consequently it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.