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Existence of Matter as a Proof of the Existence of Gravitational Torsion
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One of the reasons why Einstein-Cartan-Sciama-Kibble theory --- which includes torsion due to the intrinsic spin of matter --- is not widely accepted as a viable theory of gravity, is the lack of any experimental evidence for the gravitational torsion. But at the heart of all matter are elementary fermions, which are mathematically described as spinors, and can be viewed as defects in spacetime associated with torsion. Therefore, in this essay we argue that the existence of matter itself provides a proof that gravitational torsion exists, albeit only inside of matter, and hence it does not propagate.
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The reduced Dirac structure of General Relativity on manifolds with corners
The reduced corner phase space of Palatini–Cartan gravity is a Dirac structure—the graph of a Poisson bivector—yielding a strict BF2V theory.
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