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 EinsteinMaxwell 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
