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arXiv · gr-qc/9412029

The Momentum Constraints of General Relativity and Spatial Conformal Isometries

R. Beig·N. Ó Murchadha
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Abstract

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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R. Beig, N. Ó Murchadha. 1994-12-09. The Momentum Constraints of General Relativity and Spatial Conformal Isometries. https://doi.org/10.1007/bf02099258

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