Isometries compatible with asymptotic flatness at null infinity: A complete description

Abhay Ashtekar, Basilis C. Xanthopoulos

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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 Kabcdnd 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 languageEnglish (US)
Pages (from-to)2216-2222
Number of pages7
JournalJournal of Mathematical Physics
Volume19
Issue number10
Publication statusPublished - Dec 1 1977

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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