Structure of the gravitational field at spatial infinity. I. Asymptotically Euclidean spaces
A new formulation for the study of the asymptotic structure of a gravitational field at spatial infinity is presented. First, the disadvantages of the existing formulations are identified in order to recognize the underlying causes and exclude them from the new formulation. It is concluded that neither conformal nor projective completion should be used. From a study of the Euclidean space we obtain a method of completion of a three-dimensional space (H,g) with positive-definite metric g so that a two-dimensional boundary L is attached to the space at infinity and a three-dimensional positive definite C/sup infinity/ metric g exists near and on L. The whole method is based on replacing the conformal transformation of the conformal completion by the relation ..cap omega../sup -2/g/sup i/j-..cap omega../sup -4/g/sup i/mg/sup j/n..cap omega.. /sub ;/m..cap omega../sub ;/n=g/sup i/j-g/sup i/mg/sup j/n ..cap omega../sub vertical-barm/..cap omega../sub vertical-barn/. Thus the concept of asymptotic simplicity is defined. Then the additional conditions are determined for the space to be asymptotically Euclidean. The asymptotic symmetries and the uniqueness of the boundary are examined briefly.
- Research Organization:
- Institute of Astronomy, University of Cambridge, Cambridge, England
- OSTI ID:
- 5841589
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:1; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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