Localisation of field energy

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Abstract
The authors define conservation laws in general relativity with respect to a flat reference spacetime, via Noether's theorem and the standard Lagrangian function, quadratic in first-order derivatives. The covariant superpotential obtained in that way fulfils all standard global requirements at spatial and at null infinity and has no anomalous factor of two for the ratio of the mass to angular momentum. Next they attempt to localise the conservation laws and obtain linear and angular momentum densities. They put forward local mapping equations in which a key role is played by a family of artificial, short living, closed shells of matter whose interior is flat. The equations are derived on the basis that the linear momentum densities at each point of the flat interior must be equal to zero. They gain some insight in the mapping equations by considering static spacetimes and spaces with spherically symmetric static shells.