Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

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 Schr dinger Institute, Vienna in July 1997, at the Universit t Tübingen 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.