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In Einsteins theory of gravity the metric gives a unique torsion free connection called the Levi-Civita connection.

In the Einstein-Cartan theory we allow any connection compatible with the metric and not just the unique one that has no torsion.

Q. Why do we choose a torsion free connection in GR?

Q. What does torsion represent physically in the Einstein-Cartan theory?

Mozibur Ullah
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    I asked a related question here. – knzhou Jan 19 '19 at 22:10
  • I think the 1st of your two sub-questions is the best question I've seen on the site, and I can only relate it to "non-physical" institutional influences on physics, and especially on both the private and (thru a political system lacking restrictions on the funding of election campaigns) public branches of the university system in the U.S., overall the world's wealthiest country with anywhere near its population. Torsion's potential for eliminating the need for cosmological singularities is concisely described at https://arxiv.org/pdf/gr-qc/0606062.pdf . – Edouard Apr 25 '20 at 17:57

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