On the weakest falloff conditions in the metric for an isolated system

Abstract

The weakest asymptotic behavior in the metric for defining an asymptotically fiat spacetime at spatial infinity is obtained. The technique of the field formulation of general relativity developed earlier in the Lagrangian description is used. The properties of the latter are similar to those of an ordinary gauge field theory in a fixed background spacetime. The role of the auxiliary background is plaid by Minkowski space. Integrals Of motion are defined with the help of a stress-energy tensor of the gravitational field together with its sources and Killing vectors of the background spacetime. It is shown that the weakest asymptotics of gauge transformations, which conserve values of the integrals of motion, defines the weakest falloff conditions in the field gravitational potentials (the same, in the dynamic metric of general relativity if the ordinary geometrical formulation is used). The results are compared with the some known ones.