The Momentum Constraints of General Relativity and Spatial Conformal Isometries

Details The Momentum Constraints of General Relativity and Spatial Conformal Isometries The Momentum Constraints of General Relativity and Spatial Conformal Isometries

1994-12-09

arxiv.org/abs/gr-qc/9412029v1

Commun.Math.Phys. 176 (1996) 723-738

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages

Scientific paper

10.1007/BF02099258

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. When $g_{ab}$ has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions -- certain (combinations of) moments have to vanish -- which we study.

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