Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 4

Quasilocal angular momentum and center of mass in general relativity

Pages: 671 – 682



Po-Ning Chen (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Mu-Tao Wang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined quasi-local energy-momentum, this completes the definition of conserved quantities in general relativity at the quasi-local level. We justify this definition by showing the consistency with the theory of special relativity and expectations on an axially symmetric spacetime. The limits at spatial infinity provide new definitions for total conserved quantities of an isolated system, which do not depend on any asymptotically flat coordinate system or asymptotic Killing field. The new proposal is free of ambiguities found in existing definitions and presents the first definition that precisely describes the dynamics of the Einstein equation.

Published 4 November 2016