  The Ashtekar-Streubel fluxes give a proposed definition of the angular
momentum emitted by an isolated gravitationally radiating system. This was
based on identifying a "phase space of radiative modes," independent of any
internal degrees of freedom, and using the Hamiltonian functions conjugate to
the action of the Bondi-Metzner-Sachs (BMS) group as the energy-momentum,
supermomentum and angular momentum. However, there are some difficulties in
formulating this phase space so as to get the proper degrees of freedom. I
consider how to address this point, and also to identify circumstances in which
the radiative modes are sufficiently decoupled that they can be assigned their
own angular momentum. Two different phase spaces are considered. One, which
seems to reflect what previous workers have done (it leads to the usual
formulas for the Ashtekar-Streubel fluxes), is mathematically simpler, but this
has unwanted degrees of freedom and is difficult to interpret physically. The
second is a quotient of the first; it is better justified (at least in terms of
degrees of freedom), and plausibly decouples the radiative angular momentum
from internal modes (at least for systems which ultimately become stationary).
The symplectic form for this quotient, and the corresponding angular momentum
flux, involve highly non-local correlations. Both phase spaces are shown to
have Poisson brackets implementing the BMS algebra. For both phase spaces, for
axisymmetric space-times vacuum near null infinity, there can be no
gravitational radiation of angular momentum about the axis of symmetry,
although matter can carry off angular momentum in such cases.
