  We construct weak solutions for the evolution of hypersurfaces along their
inverse space-time mean curvature in asymptotically flat maximal initial data
sets. As the speed of the new flow is given by a space-time invariant, it can
detect both future- and past-trapped apparent horizons. The weak solution
extends concepts developed by Huisken-Ilmanen for inverse mean curvature flow
and by Moore for inverse null mean curvature flow.
