  We discuss expansions for the Cotton-York tensor near infinity for arbitrary
slices of stationary spacetimes. From these expansions it follows directly that
a necessary condition for the existence of conformally flat slices in
stationary solutions is the vanishing of a certain quantity of quadrupolar
nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus,
the Kerr metric admits no conformally flat slices. An analysis of higher orders
in the expansions of the Cotton-York tensor for solutions such that the
obstruction vanishes suggests that the only stationary solution admitting
conformally flat slices are the Schwarzschild family of solutions.
