Foundations of Physics 34 (2):211-238 (2004)

J. Brian Pitts
Cambridge University
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector formalism reduce the configuration space to the causality-respecting part. In this smaller space, gauge transformations do not form a group, but only a groupoid. The flat metric removes the difficulty of defining equal-time commutation relations in quantum gravity and guarantees global hyperbolicity.
Keywords null cones  bimetric  field formulation  causality
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DOI 10.1023/B:FOOP.0000019582.44548.6a
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Einstein׳s Equations for Spin 2 Mass 0 From Noether׳s Converse Hilbertian Assertion.J. Brian Pitts - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 56:60-69.
Absolute Objects and Counterexamples: Jones–Geroch Dust, Torretti Constant Curvature, Tetrad-Spinor, and Scalar Density.J. Brian Pitts - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (2):347-371.

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