Pitts, J. Brian (2016) Einstein's Equations for Spin 2 Mass 0 from Noether's Converse Hilbertian Assertion. [Preprint]

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Abstract
An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energymomentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action.
Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negativeenergy degrees of freedom ("ghosts") for stability, along with universal coupling: all energymomentum including gravity's serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energymomentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stressenergy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeldtinged form.
The Rosenfeld stressenergy is identically the canonical stressenergy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.
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