Energy, momentum, and center of mass in general relativity

TL;DR

This paper introduces new, physically acceptable definitions of energy, momentum, and center of mass in general relativity, resolving longstanding difficulties and aligning classical physics with Einstein's equations.

Contribution

It presents novel definitions of center of mass and angular momentum derived from first principles and geometric analysis, unifying classical and relativistic concepts.

Findings

Classical p=mv formula is consistent with Einstein's equations using new definitions.

New quasi-local and total definitions of center of mass and angular momentum.

Progress in resolving fundamental issues in defining physical quantities in general relativity.

Abstract

These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain these difficulties and progresses that have been made. In particular, I shall introduce new definitions of center of mass and angular momentum at both the quasi-local and total levels, which are derived from first principles in general relativity and by the method of geometric analysis. With these new definitions, the classical formula p=mv is shown to be consistent with Einstein's field equation for the first time. This paper is based on joint work [14][15] with Po-Ning Chen and Shing-Tung Yau.