The Newtonian limit of Penrose's quasi-local mass

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Abstract
Penrose's definition, (1982), of quasi-local mass is applied in the Newtonian limit of general relativity. The calculations are for 2-surfaces within a hypersurface of constant Newtonian time t. The leading-order terms in both the mass within the 2-surface and the difference between the mass and a conserved mass within the 2-surface are calculated. The former is just the Newtonian mass contained within the 2-surface and the latter, for a 2-surface surrounding an isolated system, gives the standard expression for the energy of the system. When applied to 2-surfaces containing parts of a system results interpretable in terms of binding energies appear.

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