On the evolution of hypersurfaces along their inverse spacetime mean curvature

TL;DR

This paper develops weak solutions for hypersurface evolution driven by inverse space-time mean curvature, capable of detecting trapped horizons, extending previous inverse mean curvature flow concepts to a spacetime setting.

Contribution

It introduces a new weak solution framework for hypersurface evolution along inverse space-time mean curvature, generalizing prior inverse mean curvature flows to include spacetime invariants.

Findings

Constructed weak solutions in asymptotically flat maximal initial data

Flow detects both future- and past-trapped apparent horizons

Extends Huisken-Ilmanen and Moore flow concepts to spacetime

Abstract

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.