Who’s “spin” is in the Einstein-Cartan theory? Source’s spin or the test particle’s spin?(adsbygoogle = window.adsbygoogle || []).push({});

I quantum mechanics, when we say spin orbit interaction, such as in hydrogen atom, it’s about the test particle's, the electron’s spin and the electron’s orbit interact to each other.

In the Einstein’s general relativity, with weak field condition, it can be described with Gravitoelectromagnetism, in which the source’s spin interacts with the test particles, that leads to the frame dragging and the Lense-Thirring effect.

Its said that “general relativity has one flaw that it cannot model spin-orbit coupling, so we need the Einstein-Cartan theory”. But who’s “spin” is here in the Einstein-Cartan theory? Source’s spin or the test particle’s spin?

From the relation,

(divergence of spin current) = P_{ab} – P_{ba} <> 0

it seems the spin is the source’s spin. Than what the difference between the Einstein-Cartan theory and Gravitoelectromagnetism? What happens if the test particle has spin?

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# Who’s spin in the Einstein-Cartan theory? Source’s or test particle's?

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