In
mathematical physics, a
closed timelike curve (
CTC) is a
world line in a
Lorentzian manifold, of a material particle in
spacetime that is "closed", returning to its starting point. This possibility was discovered by
Kurt Gödel in 1949, who discovered a solution to the equations of
general relativity (GR) allowing CTCs known as the
Gödel metric; and since then other GR solutions containing CTCs have been found, such as the
Tipler cylinder and
traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of
time travel backwards in time, raising the spectre of the
grandfather paradox, although the
Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of
quantum gravity which would replace GR, an idea which
Stephen Hawking has labeled the
chronology protection conjecture. Others note that if every closed timelike curve in a given space-time passes through an
event horizon, a property which can be called chronological censorship, then that space-time with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.