  The flux of angular momentum in electromagnetism cannot be expressed entirely
in terms of the field's radiative degrees of freedom. Its expression also
involves Coulombic pieces of the field, in the form of a charge aspect
$q(\theta,\phi)$, a function of polar angles whose integral gives the total
charge of the system. Guided by the strong analogy between radiative processes
in electromagnetism and gravitation, we ask whether the flux of angular
momentum in general relativity might also involve Coulombic pieces of the
gravitational field. Further, we ask whether such terms might have been missed
in the past by specializing the flux to sources of gravitational waves that are
at rest with respect to the frame in which the flux is evaluated. To answer
these questions we bring together the Landau-Lifshitz formulation of the
Einstein field equations, which provides specific definitions for angular
momentum and its associated flux, and the Bondi formalism, which provides a
systematic expansion of the metric of an asymptotically flat spacetime in
inverse powers of the distance away from the matter distribution. We obtain a
new expression for the flux of angular momentum, which is not restricted to
sources of gravitational waves at rest nor to periodic sources. We show that
our new expression is equivalent to the standard formula used in the literature
when these restrictions are put in place. We find that contrary to expectations
based on the analogy between electromagnetism and gravitation, the flux of
angular momentum in general relativity can be expressed entirely in terms of
the field's radiative degrees of freedom. In contrast to electromagnetism, no
Coulombic information is required to calculate the flux of angular momentum in
general relativity.
