4 Tools to Construct and Analyze the Quasi-Local Quantities
Having accepted that the gravitational energy-momentum and angular momentum should be introduced
at the quasi-local level, we next need to discuss the special tools and concepts that are needed in practice to
construct (or even to understand the various special) quasi-local expressions. Thus, first, in Section 4.1 we
review the geometry of closed spacelike 2-surfaces, with special emphasis on the so-called 2-surface data.
Then, in the remaining two Sections 4.2 and 4.3, we discuss the special situations where there is a more or
less generally accepted ‘standard’ definition for the energy-momentum (or at least for the mass) and
angular momentum. In these situations any reasonable quasi-local quantity should reduce to