Foliations by Stable Spheres with Constant Mean Curvature for Isolated Systems with General Asymptotics

TL;DR

This paper establishes the existence and uniqueness of constant mean curvature foliations in asymptotically flat initial data sets satisfying the Regge-Teitelboim condition, linking the geometric center of the foliation to the physical center of mass.

Contribution

It generalizes previous results by constructing such foliations for more general asymptotically flat manifolds satisfying the Regge-Teitelboim condition.

Findings

Foliations are asymptotically concentric with the geometric center matching the center of mass.

Existence and uniqueness of the foliation are proven under the specified conditions.

The construction extends prior work to broader classes of asymptotically flat manifolds.

Abstract

We prove the existence and uniqueness of constant mean curvature foliations for initial data sets which are asymptotically flat satisfying the Regge-Teitelboim condition near infinity. It is known that the (Hamiltonian) center of mass is well-defined for manifolds satisfying this condition. We also show that the foliation is asymptotically concentric, and its geometric center is the center of mass. The construction of the foliation generalizes the results of Huisken-Yau, Ye, and Metzger, where strongly asymptotically flat manifolds and their small perturbations were studied.