Conformal extensions for stationary spacetimes

Abstract

The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit expansions in a neighbourhood of the cylinder at spatial infinity which are analytic with respect to some suitable time, radial and angular coordinates. It is then shown that the essentials of the construction are independent of the choice of conformal gauge. As a consequence, one finds that the construction of the cylinder at spatial infinity and the regular finite initial value problem for stationary initial data sets are, in a precise sense, as regular as they could be.