  We introduce a new geometric evolution equation for hypersurfaces in
asymptotically flat spacetime initial data sets, that unites the theory of
marginally outer trapped surfaces (MOTS) with the study of inverse mean
curvature flow in asymptotically flat Riemannian manifolds. A theory of weak
solutions is developed using level-set methods and an appropriate variational
principle. This new flow has a natural application as a variational-type
approach to constructing MOTS, and this work also gives new insights into the
theory of weak solutions of inverse mean curvature flow.
