Abstract
The usual construction of anH space from asymptotic data onI+ uses only the radiative component of the asymptotic gravitational field and ignores the longitudinal part of the field [2]. While Penrose and Sparling [1] have given the construction of a deformed twistor space encoding the Schwarzschild structure by exponentiating the linearized spin 2 monopole field, one would like to have a directH space construction as a step toward constructingH spaces containing all the asymptotic degrees of freedom. The first step of giving a directH space construction for the Schwarzschild asymptotic data is contained in the following. Several interesting new structures arise in this process.
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