Bondi's vector, and the Seliger and 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 and Whitham it is shown that they are the expressions which arise most naturally in context 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 Newtonian limit. (author)