  Static spherically symmetric solutions of the Einstein's field equations in
isotropic coordinates representing perfect fluid matter distributions from
Newtonian potential-density pairs are investigated. The approach is illustrated
with three simple examples based on the potential-density pairs corresponding
to a harmonic oscillator (homogeneous sphere), the well-known Plummer model and
a massive spherical dark matter halo model with a logarithmic potential.
Moreover, the geodesic circular motion of test particles around such structures
is studied. The stability of the orbits against radial perturbations is also
analyzed using an extension of the Rayleigh criteria of stability of a fluid in
rest in a gravitational field. The models considered satisfy all the energy
conditions.
