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Motivated by the foliation by stable spheres with constant mean curvatureconstructed by Huisken-Yau, Metzger proved that every initial data set can befoliated by spheres with constant expansion (CE) if the manifold isasymptotically equal to the standard [t=0]-timeslice of the Schwarzschildsolution. In this paper, we generalize his result to asymptotically flatinitial 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.

Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry