Energy, momentum, and center of mass 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.

A paper based on the author's talk at the JDG 2014 conference on Sep 13-14, 2014. To be published in Surveys in Differential Geometry, Vol. 21 (2016)

References in corpus (8)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Conserved quantities in general relativity: from the quasi-local level to spatial infinity
• Time evolution of ADM and CMC center of mass in general relativity
• Quasilocal angular momentum and center of mass in general relativity
• Rigidity and minimizing properties of quasi-local mass
• Conserved Quantities of harmonic asymptotic initial data sets
• Explicit Riemannian manifolds with unexpectedly behaving center of mass