I've been reading up on EC theory, and the basic premise and the math behind it are all very straightforward. What I'm a little confused about is more the intuitive side of the theory, and I'm sure it stems from a very poor intuitive understanding of chirality (I do have(adsbygoogle = window.adsbygoogle || []).push({}); someintuitive understanding from the research I've done, and know all about the math behind it, but the whole thing is still pretty foreign to me on any intuitive level).

Anyway, I was wondering if someone could explain the difference between chirality and classical angular momentum in the EC framework (no quantum mechanics, chiral fields/particles do have classical descriptions). The way I see it, a chiral geodesic is a geodesic capable of describing the rotation of point particles along it. So the extra d.o.f. in the SET/metric store this extra information. With non-chiral point particles (or fields) these rotations aren't observed because the particles don't change state under rotations (i.e. a 2pi rotation leaves them unchanged)

The problem I'm having is that all the angular momentum of a system is stored in the SET, which in normal GR is symmetric. So a symmetric SET is perfectly capable of describing rotating objects, and yet for some reason you need the 6 extra d.o.f. of an asymmetric tensor to model chirality! Clearly if you take the limit as R goes to 0 of some rotating ball with radius R, the originally symmetric SET will remain symmetric. However this ball will now be a point particle with angular momentum right? I think this entire issue might just boil down to the difference between SU(2) rotations and SO(3) rotations, but then I remember that GRcandescribe effects similar to EC theory. For example, a ball with finite radiuswillrotate as it follows the geodesic of its c.o.m, and all of this can be predicted with symmetric SETs/metrics!

Also a related question: I'm aware that Kerr-Newman black holes have a lot of similarities to fundamental particles (g-factor, no hair, radius, etc.), but do they also share the same transformation properties? i.e. Do Kerr-Newman black holes transform as SU(2) under rotations? I'm thinking itcouldbe possible, if you use the fully extended space-time with the r < 0 universe, as it kind of reminds me of the plate trick demonstration

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# Einstein-Cartan theory

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