Pseudo-Minkowskian coordinates in asymptotically flat space-times

Abstract

For a rich class of asymptotically flat vacuum space-times, we show that it is possible to introduce a global coordinate system in a canonical fashion that is analogous to the standard Minkowskian coordinate systems used in flat space. This is accomplished by studying the intersection of the future light cone of interior space-time points with future null infinity. This intersection, referred to as a light cone cut of future null infinity, is piecewise a two-surface which can be described analytically by a function of the coordinates of null infinity. This function (the light cone cut function) can be given a special spherical-harmonic decomposition with the coefficients depending on the interior points. The canonical pseudo-Minkowskian coordinates are defined from the four coefficients of the $l$=0,1 spherical harmonics. In Minkowski space-time this prescription yields precisely the standard Cartesian flat coordinates.