Equations of motion for the sources of asymptotically flat spaces

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Abstract
We present an exact calculation that leads to the equations of motion (which naturally contain gravitational radiation reaction terms) of a system subject to no external forces. The novelty of our approach lies in the fact that the system is to be considered as the source of an asymptotically flat space and that all the revelant physical quantities such as the velocity νμ, 4-momentum pμ, angular momentum-center of mass tensor Sμν (as well as higher moments) are then defined in terms of surface integrals taken at infinity. A subset of the Einstein equations (equivalent to Bondi's supplemantary conditions) then yields the time-evolution equations for these variables.

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