Abstract:
Two categories of exact solutions are found to the Einstein field equations for an
anisotropic fluid sphere with a particular choice of the anisotropic factor and one of the
gravitational potentials. The condition of pressure isotropy is reduced to alinearsecond order
differential equationwhich can be solved in general.Consequentlywe can find exact solutions to
the Einstein field equations correspondingto a static spherically symmetric gravitational potential
in terms of elementaryfunctions, namely polynomials and product of polynomials andalgebraic
functions.These solutions contain particular solutions found previously includingmodels of
isotropic relativistic spheres
