1 Space-time
For it to work, an object needs to follow a world line through space-time that returns it to the same coordinates that it was at before it set off.
2 Time travel loop
A closed timelike curve is a time travel loop. Einstein said this would create a paradox – such as going back and killing your father before your birth.
3 Black holes
A spinning black hole would create a powerful gravitational field that could warp the fabric of existence and loop space-time on itself.
4 Quantum mechanics
But quantum mechanics suggests small objects – perhaps matter or information – could enter a closed timelike curve without a paradox.