Closed timelike curves (CTCs) are peculiar solutions to Einstein’s field equations in general relativity that allow for time travel—at least in theory. A CTC is a path through spacetime that loops back on itself, meaning an object following this path could return to its own past.
In a CTC:
- The object always moves forward locally in time (along a timelike path),
- But globally, it can end up at the same spacetime point it started from.
CTCs arise in certain theoretical spacetimes, such as:
- Gödel’s rotating universe, which permits global time loops
- Kerr black holes, where frame dragging might allow closed loops inside the event horizon
- Tipler cylinders and traversable wormholes, under exotic conditions
However, closed timelike curves raise deep issues:
- They lead to paradoxes, such as the famous grandfather paradox
- Their existence often requires exotic matter or violations of known energy conditions
- Most physicists believe some form of the chronology protection conjecture (proposed by Stephen Hawking) prevents them from forming in reality
While no experimental evidence supports their existence, CTCs remain a fascinating possibility in theoretical physics and a powerful lens for exploring the limits of causality, time, and the structure of the universe.