geodesic flow

Geodesic flow describes the natural movement of a point traveling along the shortest possible paths—called geodesics—on a curved surface or space. Imagine a bead sliding smoothly without friction on a curved wire; it follows a geodesic. In mathematics and physics, especially in general relativity, this concept models how objects like planets or light move under no external forces, solely influenced by the curvature of spacetime. Essentially, geodesic flow captures how objects move along natural, most efficient routes dictated by the shape of the space itself.