On the relation between metric and spin--2 form. of lin. Ein. theory

Details On the relation between metric and spin--2 form. of lin. Ein. theory On the relation between metric and spin--2 form. of lin. Ein. theory

1994-11-28

arxiv.org/abs/gr-qc/9411066v1

Gen.Rel.Grav.27:821-843,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, latex

Scientific paper

10.1007/BF02113066

A twenty--dimensional space of charged solutions of spin--2 equations is proposed. The relation with extended (via dilatation) Poincar\'e group is analyzed. Locally, each solution of the theory may be described in terms of a potential, which can be interpreted as a metric tensor satisfying linearized Einstein equations. Globally, the non--singular metric tensor exists if and only if 10 among the above 20 charges do vanish. The situation is analogous to that in classical electrodynamics, where vanishing of magnetic monopole implies the global existence of the electro--magnetic potentials. The notion of {\em asymptotic conformal Yano--Killing tensor} is defined and used as a basic concept to introduce an inertial frame in General Relativity via asymptotic conditions at spatial infinity. The introduced class of asymptotically flat solutions is free of supertranslation ambiguities.

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