What about lightlike geodesics? Do they converge, diverge, or remain equally spaced? That’s tricky, because in 2D spacetime the only direction perpendicular to a lightlike geodesic is along the geodesic itself, so you can’t measure the separation along a perpendicular vector.
Here lightlike geodesics grow further apart, as measured along the grey circles. This is how the cosmological red shift works: wavefronts in an expanding universe move apart. But that’s a measurement by *particular observers*, at rest in galaxies that are themselves moving apart.
