spintorsion

Spintorsion is a concept in certain gravitational theories in which the intrinsic spin of matter fields interacts with spacetime torsion. It is most closely associated with Einstein–Cartan theory, a modification of general relativity formulated in a Riemann–Cartan geometric setting where the affine connection has an antisymmetric part called torsion. In this framework, spin density acts as a source for torsion, while energy–momentum remains the source for curvature.

In the Einstein–Cartan field equations, torsion is typically not a propagating field; it is algebraically related to the spin density of matter. As a result, torsion vanishes in regions with no spin, such as vacuum, and spin–torsion effects are most relevant at very high densities. The presence of torsion leads to a four-fermion contact interaction when the torsion field is integrated out, effectively producing a spin–spin coupling between fermions.

The physical implications of spintorsion include potential modifications to the behavior of matter under extreme conditions, such as the early universe or in highly compact objects. Some models suggest that spin–torsion interactions could influence collapse dynamics or avoid certain types of singularities, though these results are model-dependent. In everyday conditions, torsion-induced effects are extremely small and difficult to detect.

Experimental and observational status remains inconclusive, with no confirmed detection of spacetime torsion. Constraints come from precision gravity experiments and spin-precession measurements, which place tight bounds on possible torsion couplings.

See also: Einstein–Cartan theory, torsion, spinor, Riemann–Cartan geometry.