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Bondi’s vector, and the Seliger & Whitham Variational Principle for matter fields

Bondi’s Newtonian Poynting Vector is extended to other ‘Bondi-type’ conserved quantities, which are also derived by variational methods. By means of the technique of Seliger & Whitham it is shown that they are the expressions which arise most naturally in contexts concerned with the equations of motion. The pseudo-tensor derived from the Lagrangian R√(— g) is the corresponding expression in General Relativity; direct calculation verifies that it tends to Bondi’s vector in the Newtonian limit.