The Existence of Maximal Slicings in Asymptotically Flat Spacetimes

Cantor, M., A. Fischer, J. E. Marsden, N. O Murchadha and J. York

Commun. math. Phys., 49, (1976), 187-190

Abstract:

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