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Null Cones and Einstein's Equations in Minkowski Spacetime

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Abstract

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.

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  1. J. Brian Pitts

    Present address: Program in History and Philosophy of Science, University of Notre Dame, 346 O'Shaughnessy, Notre Dame, Indiana, 46556

Authors and Affiliations

  1. The Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, Department of Physics, The University of Texas at Austin, Austin, Texas, 78712

    J. Brian Pitts

  2. Mathematics Department, St. Edward's University, Austin, Texas, 78704

    J. Brian Pitts

  3. The Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Austin, Texas, 78712

    W. C. Schieve

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Pitts, J.B., Schieve, W.C. Null Cones and Einstein's Equations in Minkowski Spacetime. Foundations of Physics 34, 211–238 (2004). https://doi.org/10.1023/B:FOOP.0000019582.44548.6a

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