General relativity contains exact solutions—such as Gödel's rotating universe and the Kerr black hole metric—that feature closed timelike curves (CTCs), which worldlines loop back on themselves and would allow travel to the past.

In 1949, mathematician Kurt Gödel discovered a solution to Einstein's field equations representing a rotating universe. In this model, the rotation of matter creates a global spacetime structure where certain trajectories curve back to their own past, forming CTCs. Later, Roy Kerr's 1963 solution for rotating black holes also showed that inside the inner horizon, spacetime geometry permits CTCs. These mathematical constructs do not violate the equations of general relativity; they simply describe highly exotic spacetimes where the past is reachable by following a continuous path through space and time. However, whether such spacetimes can exist in our universe remains an open question, as they require conditions like universal rotation or infinite density that may not be physically realizable.