Quasi-local energy-momentum and angular momentum in general relativity

Abstract

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned. This review is based on talks given at the Erwin Schr̈odinger Institute, Vienna in July 1997, at the Universiẗat T̈ubingen in May 1998, and at the National Center for Theoretical Sciences in Hsinchu, Taiwan and at the National Central University, Chungli, Taiwan, in July 2000.