  Motivated by the foliation by stable spheres with constant mean curvature
constructed by Huisken-Yau, Metzger proved that every initial data set can be
foliated by spheres with constant expansion (CE) if the manifold is
asymptotically equal to the standard [t=0]-timeslice of the Schwarzschild
solution. In this paper, we generalize his result to asymptotically flat
initial data sets and weaken additional smallness assumptions made by Metzger.
Furthermore, we prove that the CE-surfaces are in a well-defined sense
(asymptotically) independent of time if the linear momentum vanishes.
