On the structure of spatial infinity. II. Geodesically regular Ashtekar–Hansen structures

The ambiguities in the differentiable structure of Ashtekar–Hansen completions satisfying a geodesic condition are analyzed. The results obtained imply, in particular, uniqueness up to a four-parameter family of ‘‘logarithmic transformations’’ of completions of asymptotically flat space-times stationary ‘‘in a neighborhood of i0.’’