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Insights General Relativity as a Gauge Theory - Comments

  1. Nov 1, 2016 #21


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    Mmmm, I have to think about that, since this point arises in all dimensions.
  2. Nov 8, 2016 #22
    I was not implying otherwise just pointing to the similarity of concept with the gravitational anomaly specifically in the 4-spacetime and even though what you explained about Poincare gauge theory of gravity is not limited to a certain dimensionality, it makes little sense to apply it for instance to the 2+1 GR that in vacuum is trivially flat(no weyl curvature so it's pretty worthless physically.

    I have another question, with the gauge procedure described in the insight article, starting from Minkowski 4 spacetime and gauging and getting rid of the translations by making torsion vanish, a gravitational vacuum is obtained that is equivalent to the GR equations in vacuum, i.e. to the Schwarzschild metric, but is not singular(just like Einstein-Cartan gravity theory is not singular), so this is a gauge from wich black hole physics is not obtainable even if the classical tests of relativity are. I was under the impression that any gravitational theory of the vacuum with rotational symmetry, that can be expressed as Rab=0 would give the singular Schwarzschild solution, per Birkhoff's theorem, so I'm not sure what exactly I'm overlooking.
  3. Nov 8, 2016 #23


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    There are many more vacuum solutions of Einstein's field equations than just the Schwarzschild solution, e.g., the Friedmann-Lemaitre-Robertson-Walker solution that is utmost important for cosmology. These solutions have no black-hole singularities but rather a big bang/crunch singularity. Of course another solution is Minkowski spacetime which has no sinularities at all.
  4. Nov 8, 2016 #24


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    The cosmological solutions are usually non-vacuum. I assume you meant something else than what you wrote.
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