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The first flux term is identical to that calculated from classical electromagnetic theory
Remark 13. In the past, most discussions of angular momentum make use of group theoretical
ideas with Noether theorem type arguments, via the BMS group and the Lorentz subgroup, to define
angular momentum. Unfortunately this has been beset with certain difficulties; different authors get
slightly different numerical factors in their definitions, with further ambiguities arising from the
supertranslation freedom of the BMS group. (See the discussion after Eq. (2.62)) Our approach is
very different from the group theoretical approach in that we come to angular momentum directly
from the dynamics of the Einstein equations (the asymptotic Bianchi Identities). We use the angular
momentum definition from linear theory, Eq. (2.62
), (agreed to by virtually all) and then supplement
it via conservation equations (the flux law) obtained directly from the Bianchi Identities. We have a
unique one-parameter family of cuts coming from the complex world line defining the complex center
of mass. This is a geometric structure with no ambiguities. However, another ambiguity does arise
by asking which Bondi frame should be used in the description of angular momentum; this is the
ambiguity of what coordinate system to use.
http://www.livingreviews.org/lrr-2012-1 |
Living Rev. Relativity 15, (2012), 1
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