Spatial infinity as a boundary of spacetime

Abstract

A definition of asymptotic flatness at spatial infinity is given by imposing conditions at a time-like boundary of a completed 4-manifold. The resulting framework is similar to the Penrose description of asymptotic flatness at null infinity in that physics at spatial infinity is coded in smooth tensor fields on the boundary. it reproduces the standard results of the i⁰-framework with the advantage that it avoids the awkward differentiability conditions imposed at i⁰. The universal structure made available by the definition is examined and the structure of the associated asymptotic symmetry group is analysed. The tensor fields describing the leading order behaviour of the gravitational field at spatial infinity are then introduced and the field equations that they satisfy are derived. Finally, the expressions of the 4-momentum and the angular momentum are presented. The structure of the permissible isometry groups in asymptotically flat spacetimes is discussed in an appendix.