Closed time-like curves

Closed time-like curves (CTCs) are theoretical paths in spacetime that loop back on themselves, allowing an object or information to return to an earlier point in time. Imagine a circle in time instead of a straight line; if you could travel along this circle, you could revisit your own past. CTCs arise in the context of general relativity, particularly in solutions involving rotating black holes or certain cosmic structures. While fascinating, their existence raises complex paradoxes, such as the famous "grandfather paradox," challenging our understanding of causality and the nature of time itself.