Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
Let \(N\) be a three-dimensional Riemannian manifold with one end diffeomorphic to \(\mathbb{R}^3\setminus B_1(0)\) such that the metric on \(N\) asymptotically approaches the Euclidean metric near infinity: \(g_{ij} = (1 + 2m/r) \delta_{ij} + O(-r^2)\). By constructing a unique constant mean curvature foliation in the exterior region, there is defined a geometric center of mass at infinity for asymptotically flat ends provided that the mass \(m\) of \(g\), measuring the deviation of \(g\) from the flat metric at infinity, satisfies \(m > 0\). The foliation is interpreted as a geometric center of mass for an infinitely far observer.
scientific article; zbMATH DE number 866093