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A twenty--dimensional space of charged solutions of spin--2 equations isproposed. The relation with extended (via dilatation) Poincar\'e group isanalyzed. Locally, each solution of the theory may be described in terms of apotential, which can be interpreted as a metric tensor satisfying linearizedEinstein equations. Globally, the non--singular metric tensor exists if andonly if 10 among the above 20 charges do vanish. The situation is analogous tothat in classical electrodynamics, where vanishing of magnetic monopole impliesthe global existence of the electro--magnetic potentials. The notion of {\emasymptotic conformal Yano--Killing tensor} is defined and used as a basicconcept to introduce an inertial frame in General Relativity via asymptoticconditions at spatial infinity. The introduced class of asymptotically flatsolutions is free of supertranslation ambiguities.Comment: 20 pages, late

The relation between metric and spin-2 formulations of linearized Einstein theory