Riemann-Cartan geometry

Riemann-Cartan geometry is a mathematical framework that extends traditional geometry used in understanding spacetime. Unlike standard geometry, which describes curved spaces with no torsion, Riemann-Cartan geometry incorporates torsion—a kind of "twist" in the fabric of space. This approach treats gravity not only as curvature, as in Einstein’s general relativity, but also allows for torsion to influence spacetime. It’s useful in theories seeking to unify gravity with quantum mechanics and in describing how spin and intrinsic angular momentum of particles might interact with the underlying geometry of the universe.