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A framework is developed which quantifies the local exchange of energy andmomentum between matter and the linearized gravitational field. We derive theunique 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 unavoidablyremoved. The gravitational energy-momentum tensor is then shown to have twoexceptional properties: (a) it is gauge-invariant for gravitationalplane-waves, (b) for arbitrary transverse-traceless fields, the energy-densityis never negative, and the energy-flux is never spacelike. We analyse in detailthe local gauge invariant energy-momentum transferred between the gravitationalfield and an infinitesimal point-source, and show that these invariants dependonly on the transverse-traceless components of the field. As a result, we areled to a natural gauge-fixing program which at last renders the energy-momentumof the linear gravitational field completely unambiguous, and additionallyensures that gravitational energy is never negative nor flows faster thanlight. Finally, we calculate the energy-momentum content of gravitationalplane-waves, the linearized Schwarzschild spacetime (extending to arbitrarystatic linear spacetimes) and the gravitational radiation outside two compactsources: a vibrating rod, and an equal-mass binary.

Localizing the Energy and Momentum of Linear Gravity