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

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Einstein-Cartan theory

Tags:

Loading...

Similar Threads - Einstein Cartan theory | Date |
---|---|

A 'hypermomentum' and 'Belinfante–Rosenfeld tensor' -- Are they the same object? | Feb 6, 2017 |

Dynamical definition of spin tensor- Einstein Cartan theory | Nov 3, 2015 |

Who’s spin in the Einstein-Cartan theory? Source’s or test particle's? | Aug 2, 2011 |

Torsion in GR and Einstein-Cartan theory | Aug 1, 2011 |

Einstein-Cartan Theory | Mar 16, 2007 |

**Physics Forums - The Fusion of Science and Community**