Conserved quantities in general relativity: from the quasi-local level to spatial infinity

Understand

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime.

• To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group is assigned.
• Quasi-local angular momentum and quasi-local center of mass correspond to pairing this element with rotation Killing fields and boost Killing fields, respectively.
• They obey classical transformation laws under the action of the Poincar\'e group.