Nonsingularity of Flat Robertson–Walker Models in the Special Relativistic Approach to Einstein's Equations


Recently the neglected issue of the causal structure in the flat space-time approach to Einstein's theory of gravity has been substantially resolved. Consistency requires that the flat metric's null cone be respected by the null cone of the effective curved metric. While consistency is not automatic, thoughtful use of the naive gauge freedom resolves the problem. After briefly recapitulating how consistent causality is achieved, we consider the flat Robertson–Walker Big Bang model. The Big Bang singularity in the spatially flat Robertson–Walker cosmological model is banished to past infinity in Minkowski space-time. A modified notion of singularity is proposed to fit the special relativistic approach, so that the Big Bang becomes nonsingular.

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  1. 1.

    J. B. Pitts and W. C. Schieve, Gen. Rel. Grav. 33, 1319(2001); gr-qc/0101058.

    Google Scholar 

  2. 2.

    J. B. Pitts and W. C. Schieve, “Null cones in Lorentz-covariant general relativity, ” gr-qc/0111004 (2002).

  3. 3.

    R. Wald, General Relativity (University of Chicago Press, Chicago, 1984).

    Google Scholar 

  4. 4.

    R. Sorkin, “An example relevant to the Kretschmann–Einstein debate, ” (2002).

  5. 5.

    P. Hahn, Trans. Amer. Math. Soc. 242, 1(1978).

    Google Scholar 

  6. 6.

    J. Renault, A Groupoid Approach to C*-Algebras (Springer, Berlin, 1980).

    Google Scholar 

  7. 7.

    A. Ramsay, Adv. Math. 6, 253(1971).

    Google Scholar 

  8. 8.

    C. W. Misner, Phys. Rev. A 186, 1328(1969).

    Google Scholar 

  9. 9.

    A. G. Agnese and A. Wataghin, Lett. Nuov. Cim. 1, 857(1971).

    Google Scholar 

  10. 10.

    J.-M. Levy-Leblond, Amer. J. Phys. 58, 156(1990).

    Google Scholar 

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Pitts, J.B., Schieve, W.C. Nonsingularity of Flat Robertson–Walker Models in the Special Relativistic Approach to Einstein's Equations. Foundations of Physics 33, 1315–1321 (2003).

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  • bimetric
  • causality principle
  • null cones
  • cosmological singularity