The Momentum Constraints of General Relativity and Spatial Conformal Isometries

Abstract

Transverse-tracefree (TT-) tensors on $({\mathbf{R}}^3,g_{ab})$, 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.

16 pages

References in corpus (1)

• Initial Data for General Relativity with Toroidal Conformal Symmetry

Cited by in corpus (16)

• Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
• Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions
• Boundary effects in General Relativity with tetrad variables
• On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Initial data for a head on collision of two Kerr-like black holes with close limit
• On the roots of the Poincare structure of asymptotically flat spacetimes
• On the existence of initial data containing isolated black holes
• Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
• Initial data for fluid bodies in general relativity
• Black Hole Interaction Energy
• Rough solutions of the Einstein constraint equations with nonconstant mean curvature
• Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity
• Dain's invariant on non-time symmetric initial data sets
• On smoothness-asymmetric null infinities
• Asymptotically flat and regular Cauchy data