  A conserved stress energy tensor for weak field gravitational waves
propagating in vacuum is derived directly from the linearized wave equation
alone, for an arbitrary gauge using standard general relativity. In any
harmonic gauge, the form of the tensor leads directly to the classical
expression for the outgoing wave energy. The method described here, however, is
a much simpler, shorter, and more physically motivated approach than is the
customary procedure, which involves a lengthy and cumbersome second-order (in
wave-amplitude) calculation starting with the Einstein tensor. Our method has
the added advantage of exhibiting the direct coupling between the outgoing
energy flux in gravitational waves and the work done by the gravitational field
on the sources. For nonharmonic gauges, the directly derived wave stress tensor
has an apparent index asymmetry. This coordinate artefact may be removed, and
the symmetrized (still gauge-invariant) tensor then takes on its widely-used
form. Angular momentum conservation follows immediately. For any harmonic
gauge, however, the stress tensor is manifestly symmetric from the start and
its derivation depends, in its entirety, on the structure of the linearized
wave equation.
