  Exact stationary axially symmetric solutions of the 4D Einstein equations
with corotating pressureless perfect fluid sources are studied. A particular
solution with approximately flat rotation curve is discussed in some detail. We
find that simple Newtonian arguments overestimate the amount of matter needed
to explain these curves by more than 30%. The crucial insight gained by this
model is that the Newtonian approximation breaks down globally, even though it
is valid locally everywhere. No conflict with solar system tests arises.
