Closed Timelike Curves in a Rotating Universe (2D)

The Gödel metric is an exact 1949 solution to Einstein's field equations describing a universe filled with rotating dust. Because spacetime itself is dragged around the rotation axis, the geometry has a genuinely strange property: past a precise critical radius R꜀ = a√2·ln(1+√2), a simple circle traced at constant coordinate time stops being a spatial loop and becomes a timelike curve — a path a real observer could follow that returns to its own past. This top-down companion renders the exact g_φφ metric component live as you change the rotation scale a and the orbit radius R, tilts a ring of light-cone markers by the real frame-dragging term, and traces a test worldline that spirals outward in coordinate time to stay causal inside R꜀, but closes into a flat, repeating loop the moment it crosses into the closed-timelike-curve region beyond R꜀.