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The momentum constraints of general relativity and spatial conformal isometries

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Abstract

Transverse-tracefree (TT-) tensors on (R 3,g ab), withg 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. Wheng 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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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria

    R. Beig

  2. Physics Department, University College Cork, Cork, Ireland

    N. Ó. Murchadha

Authors
  1. R. Beig
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  2. N. Ó. Murchadha
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Communicated by S.-T. Yau

Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P9376-PHY.

Partially supported by Forbairt Grant SC/94/225.

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Beig, R., Murchadha, N.Ó. The momentum constraints of general relativity and spatial conformal isometries. Commun.Math. Phys. 176, 723–738 (1996). https://doi.org/10.1007/BF02099258

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