Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry

TL;DR

This paper extends the construction of constant expansion foliations from asymptotically Schwarzschild manifolds to more general asymptotically flat initial data sets, removing previous smallness constraints and analyzing their time independence under zero linear momentum.

Contribution

It generalizes Metzger's results to broader asymptotically flat settings and establishes conditions for the time independence of CE-surfaces.

Findings

CE-surfaces exist in broader asymptotically flat manifolds

CE-surfaces are asymptotically independent of time when linear momentum vanishes

Weaker assumptions than previous works are sufficient for existence

Abstract

Motivated by the foliation by stable spheres with constant mean curvature constructed by Huisken-Yau, Metzger proved that every initial data set can be foliated by spheres with constant expansion (CE) if the manifold is asymptotically equal to the standard [t=0]-timeslice of the Schwarzschild solution. In this paper, we generalize his result to asymptotically flat initial data sets and weaken additional smallness assumptions made by Metzger. Furthermore, we prove that the CE-surfaces are in a well-defined sense (asymptotically) independent of time if the linear momentum vanishes.