On the Center of Mass of Isolated Systems with General Asymptotics

TL;DR

This paper introduces a new, coordinate-free definition of the center of mass for asymptotically flat manifolds satisfying the Regge-Teitelboim condition, ensuring consistency with existing definitions and supported by a new density theorem.

Contribution

It provides a novel, natural, coordinate-free definition of center of mass for certain manifolds, aligning with prior concepts and backed by a new density theorem.

Findings

Definition is coordinate-free and natural.

Consistent with previous definitions by Corvino, Schoen, Huisken, and Yau.

Established a new density theorem for data satisfying the Regge-Teitelboim condition.

Abstract

We propose a definition of center of mass for asymptotically flat manifolds satisfying Regge-Teitelboim condition at infinity. This definition has a coordinate-free expression and natural properties. Furthermore, we prove that our definition is consistent both with the one proposed by Corvino and Schoen and another by Huisken and Yau. The main tool is a new density theorem for data satisfying the Regge-Teitelboim condition.