### Abstract

The following results concerning isometrics of space-times which are asymptotically empty and flat at null infinity are established: (i) The isometry group is necessarily a subgroup of the Poincaré group; (ii) if the asymptotic Weyl curvature is nonzero - more precisely, in the standard notation, if K_{abcd}n^{d} does not vanish identically on ℐ - the space-time cannot admit more than two Killing fields unless the metric is Schwarzschildean in a neighborhood ℐ, if it does admit two Killing fields, they necessarily commute; one (and only one) of them is a translation; the radiation field as well as the Bondi news vanishes everywhere on ℐ; and, finally, if the translational Killing field is timelike in a neighborhood of ℐ, the other Killing field is necessarily rotational. Several implications of these results are pointed out.

Original language | English (US) |
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Pages (from-to) | 2216-2222 |

Number of pages | 7 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 10 |

Publication status | Published - Dec 1 1977 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*19*(10), 2216-2222.