  We recently developed a local description of the energy, momentum and angular
momentum carried by the linearized gravitational field, wherein the
gravitational energy-momentum tensor displays positive energy-density and
causal energy-flux, and the gravitational spin-tensor describes purely spatial
spin. We now investigate the role these tensors play in a broader theoretical
context, demonstrating for the first time that (a) they do indeed constitute
Noether currents associated with the symmetry of the linearized gravitational
field under translation and rotation, and (b) they are themselves a source of
gravity, analogous to the energy-momentum and spin of matter. To prove (a) we
construct a Lagrangian for linearized gravity (a covariantized Fierz-Pauli
Lagrangian for a massless spin-2 field) and show that our tensors can be
obtained from this Lagrangian using a standard variational technique for
calculating Noether currents. This approach generates formulae that uniquely
generalize our gravitational energy-momentum tensor and spin tensor beyond
harmonic gauge: we show that no other generalization can be obtained from a
covariantized Fierz-Pauli Lagrangian without introducing second derivatives in
the energy-momentum tensor. We then construct the Belinfante energy-momentum
tensor associated with our framework (combining spin and energy-momentum into a
single object) and as our first demonstration of (b) we establish that this
Belinfante tensor appears as the second-order contribution to a perturbative
expansion of the Einstein field equations. By considering a perturbative
expansion of the Einstein-Cartan field equations, we then demonstrate that (b)
can be realized without forming the Belinfante tensor: our energy-momentum
tensor and spin tensor appear as the quadratic terms in separate field
equations, generating gravity as distinct entities. Finally, we examine the
role of...
