Generating potentials via difference equations

TL;DR

This paper derives an exact solution to Einstein's field equations for spherically symmetric charged and uncharged matter, using a difference equation approach, extending previous isotropic models and providing a realistic relativistic stellar model.

Contribution

It introduces a novel method of solving Einstein's equations via recurrence relations, extending isotropic models to include charge and barotropic equations of state.

Findings

Metric functions are well-behaved, suitable for relativistic stars.

The model admits a barotropic equation of state close to a polytrope.

Provides an exact, general solution to the Einstein field equations.

Abstract

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric functions, energy density and pressure are well behaved which suggests that this model could be used to describe a relativistic sphere. The model admits a barotropic equation of state which approximates a polytrope close to the stellar centre.