Constant scalar curvature hypersurfaces in $(3+1)$-dimensional GHMC Minkowski spacetimes

摘要

We prove that every $(3+1)$-dimensional flat GHMC Minkowski spacetime whichis not a translation spacetime or a Misner spacetime carries a unique foliationby spacelike hypersurfaces of constant scalar curvature. In otherwords, weprove that every such spacetime carries a unique time function with isochronesof constant scalar curvature. Furthermore, this time function is a smoothsubmersion.