Abstract:
We find new classes of exact solutions to the Einstein-Maxwell system of equa-
tions for a charged sphere with a particular choice of the electric field intensity
and one of the gravitational potentials. The condition of pressure isotropy is
reduced to a linear, second order differential equation which can be solved in
general. Consequently we can find exact solutions to the Einstein-Maxwell field
equations corresponding to a static spherically symmetric gravitational potential
in terms of hypergeometric functions. It is possible to find exact solutions which
can be written explicitly in terms of elementary functions, namely polynomials
and product of polynomials and algebraic functions. Uncharged solutions are
regainable with our choice of electric field intensity; in particular we generate
the Einstein universe for particular parameter values.
