R. Beig, N. O Murchadha
The Momentum Constraints of General Relativity and Spatial Conformal Isometries
The paper is published: Commun. Math. Phys. 176, 3 (1996) 723-738

MSC:

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C40 Gravitational energy and conservation laws; groups of motions

83C25 Approximation procedures, weak fields

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.

Keywords: momentum constraints, spatial conformal isometries, gravitational energy, asymptotic structure, decay at infinity