ASYMPTOTICALLY FLAT SPACETIMES AT SPATIAL INFINITY: THE FIELD APPROACH AND THE LAGRANGIAN DESCRIPTION

Abstract

An asymptotically flat spacetime (AFST) at spatial infinity is studied. The technique of the field formulation of general relativity developed earlier is used. The properties of the latter are similar to those of an ordinary gauge field theory in a fixed background spacetime. We give a definition of an AFST. The role of a background is played by Minkowski space. Integrals of motion are defined with the use of a stress-energy tensor of the gravitational field together with its sources and Killing vectors of the background spacetime. For each of the following AFST characteristics, namely the definition and the values of the integrals of motion and the action integral, we have found the weakest asymptotics for gauge transformations such that this characteristic does not change under the gauge transformations. These three kinds of falloff conditions are compared. The suggested approach is discussed and compared with some known results and methods.