The Existence of Maximal Slicings in Asymptotically Flat Spacetimes

We consider Cauchy data (g,π) on IR^3 that are asymptotically Euclidean and that satisfy the vacuum constraint equations of general relativity. Only those (g,π) are treated that can be joined by a curve of sufficiently bounded initial data to the trivial data (d, 0). It is shown that in the Cauchy developments of such data, the maximal slicing condition tr π=0 can always be satisfied. The proof uses the recently introduced weighted Sobolev spaces of Nirenberg, Walker, and Cantor.