Warning: lots of jargon ahead. I really wish I understood this better, but the sense I've gotten is that intrinsic spin needs to couple to gravitation through

Warning: lots of jargon ahead. I really wish I understood this better, but the sense I've gotten is that intrinsic spin needs to couple to gravitation through torsion rather than through the usual curvature we study in GR. Most GR courses and textbooks barely mention torsion at all: IIRC Wald for example specifies "torsion free" as a condition on derivative operators and basically doesn't ever explore the alternative (I think there's a homework problem on it). The torsion free condition is what guarantees that Christoffel symbols are symmetric in their lower indices. Once upon a time while trying to understand all this back in grad school, I wrote up a set of notes extending Wald's calculations of curvature to include the possibility of torsion. I never tried to publish them anywhere, since of course it's nothing new or groundbreaking, but they're on my website here: http://www.slimy.com/~steuard/teaching/tutorials/GRtorsion.pdf http://www.slimy.com/~steuard/teaching/tutorials/GRtorsion.p... Those notes do not discuss the connection to spin, because I was only halfway aware of it at the time and because I didn't have the time to delve into it enough to figure it out. (I also didn't know at the time that this is often called "Einstein-Cartan theory".) One notable thing about torsion is that it's a non-propagating field: as I recall, it's only non-zero inside the material with spin. I'm not entirely sure what the effects of all that might be. This 1976 review article has been lurking at the back of my to-read pile for ages: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.48.393 https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.48.... I have no idea whatsoever whether any of that is useful for making warp drives or for metric engineering. But I figured I'd share, since it seemed relevant.