Localizing the Energy and Momentum of Linear Gravity
  A framework is developed which quantifies the local exchange of energy and
momentum between matter and the linearized gravitational field. We derive the
unique gravitational energy-momentum tensor consistent with this description,
and find that this tensor only exists in the harmonic gauge. Consequently,
nearly all the gauge freedom of our framework is naturally and unavoidably
removed. The gravitational energy-momentum tensor is then shown to have two
exceptional properties: (a) it is gauge-invariant for gravitational
plane-waves, (b) for arbitrary transverse-traceless fields, the energy-density
is never negative, and the energy-flux is never spacelike. We analyse in detail
the local gauge invariant energy-momentum transferred between the gravitational
field and an infinitesimal point-source, and show that these invariants depend
only on the transverse-traceless components of the field. As a result, we are
led to a natural gauge-fixing program which at last renders the energy-momentum
of the linear gravitational field completely unambiguous, and additionally
ensures that gravitational energy is never negative nor flows faster than
light. Finally, we calculate the energy-momentum content of gravitational
plane-waves, the linearized Schwarzschild spacetime (extending to arbitrary
static linear spacetimes) and the gravitational radiation outside two compact
sources: a vibrating rod, and an equal-mass binary.
