Abstract
This talk is concerned with the implementation, in a non-time symmetric setting, of Friedrich's regular value problem near spatial infinity for the Conformal Einstein equations. Computer algebra methods are used to calculate a particular type of asymptotic expansions and to deduce a hierarchy of obstructions to the smoothness of null infinity. These calculations show, for example, that the development of Bowen-York initial data does not admit a smooth null infinity (if any). The relevance of these calculations on the light of the so-called Penrose's proposal is discussed.