Abstract:
We find new classes of exact solutions to the Einstein-Maxwell system of
equations for a charged and anisotropic sphere with a particular choice of the
electric field intensity, anisotropic factor and one of the gravitational potentials.
The condition of pressure isotropy is reduced to a linear, second order differential
equation in terms of the remaining gravitational potentials which can be solved in
general. This is achieved by transforming the corresponding field equation to a
hypergeometric equation with suitable transformations. Consequently we found
exact solutions to the Einstein-Maxwell field equations to a static spherically
symmetric gravitational potential in terms of hypergeometric functions. An
interesting feature of the class of solutions is that one can easily switch off the
electric and/or anisotropic effects in this formulation. We demonstrate that it is
possible to express our class of solutions in a simple closed form so as to examine
its physical viability for the studies of relativistic compact stars
