Insights General Relativity as a Gauge Theory - Comments

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1. Nov 1, 2016

haushofer

Mmmm, I have to think about that, since this point arises in all dimensions.

2. Nov 8, 2016

RockyMarciano

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

vanhees71

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

martinbn

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