Abstract:
In this work we study spherically symmetric space times which are static with the perfect
fluid source and an electromagnetic field with pressure anisotropy. Our intention is to
generate exact solutions to the Einstein-Maxwell system that model the interior of relativistic
stars. The field equations are obtained in detail for neutral and charged perfect fluids with
anisotropic pressure. A class of exact solutions to the field equations is generated as an
infinite series by solving the relevant difference equations. This is achieved by specifying
particular forms for one of the gravitational potentials in terms of spheroidal parameter,
electric field and the anisotropic factor. We obtain two distinct types of linearly independent
solutions, namely polynomial and algebraic forms, by restricting the spheroidal parameter
and the two constants related to the electric field and anisotropic factor. We then present the
general solutions in terms of elementary functions, from which we regain two particular
solutions reported previously for the uncharged isotropic star. In addition, a new closed form
solution is obtained and we briefly discuss the physical viability of our solution. These new
classes of solutions provide deeper insight into how charge and pressure anisotropy influence
stellar structure and stability, offering physically meaningful models for realistic compact
stars. We emphasise that our simple approach of utilising the series method of Frobenius
yields a rich family of Einstein-Maxwell solutions in terms of elementary functions.
