THE RELATION BETWEEN METRIC AND SPIN-2 FORMULATIONS OF LINEARIZED EINSTEIN THEORY

A twenty-dimensional space of charged solutions of spin-a equations is proposed. The relation with extended (via dilatation) Poincare group is analyzed. Locally, each solution of the theory may be described in terms of a potential, which can be interpreted as a metric tenser sati sfying linearized Einstein equations. Globally, the nonsingular metric tenser exists if and only if 10 among the above 20 charges do vanish. The situation is analogous to that in classical electrodynamics, wher e vanishing of magnetic monopole implies the global existence of the e lectromagnetic potentials. The notion of asymptotic conformal Yano-Kil ling tenser is defined and used as a basic concept to introduce an ine rtial frame in General Relativity via asymptotic conditions at spatial infinity. The introduced class of asymptotically flat solutions is fr ee of supertranslation ambiguities.