The Newtonian limit of orthonormal frames in metric theories of gravity

Abstract

We extend well-known results on the Newtonian limit of Lorentzian metrics to orthonormal frames. Concretely, we prove that, given a one-parameter family of Lorentzian metrics that in the Newtonian limit converges to a Galilei structure, any family of orthonormal frames for these metrics converges pointwise to a Galilei frame, assuming that the two obvious necessary conditions are satisfied: the spatial frame must not rotate indefinitely as the limit is approached, and the frame's boost velocity with respect to some fixed reference observer needs to converge.

12.5+3+1.5 pages (main text + references + appendix), to appear in General Relativity and Gravitation. v2: reference updated. v3: extended results, added references. v4: extended results. v5: corrected lemma

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