Closed timelike curve
This possibility was first discovered by Willem Jacob van Stockum in 1937[1] and later confirmed by Kurt Gödel in 1949,[2] 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.
Others note that if every closed timelike curve in a given spacetime passes through an event horizon, a property which can be called chronological censorship, then that spacetime with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.
[3] When discussing the evolution of a system in general relativity, or more specifically Minkowski space, physicists often refer to a "light cone".
This is commonly represented on a graph with physical locations along the horizontal axis and time running vertically, with units of
axis, but to an external observer it appears it is accelerating in space as well—a common situation if the object is in orbit, for instance.
In extreme examples, in spacetimes with suitably high-curvature metrics, the light cone can be tilted beyond 45 degrees.
Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions.
These include: Some of these examples are, like the Tipler cylinder, rather artificial, but the exterior part of the Kerr solution is thought to be in some sense generic, so it is rather unnerving to learn that its interior contains CTCs.
It is impossible to determine based only on knowledge of the past whether or not something exists in the CTC that can interfere with other objects in spacetime.
A CTC therefore results in a Cauchy horizon, and a region of spacetime that cannot be predicted from perfect knowledge of some past time.
The existence of CTCs would arguably place restrictions on physically allowable states of matter-energy fields in the universe.
Propagating a field configuration along the family of closed timelike worldlines must, according to such arguments, eventually result in the state that is identical to the original one.
If Deutsch's prescription holds, the existence of these CTCs implies also equivalence of quantum and classical computation (both in PSPACE).
[9] Associated with each closed null geodesic is a redshift factor describing the rescaling of the rate of change of the affine parameter around a loop.
Because of this redshift factor, the affine parameter terminates at a finite value after infinitely many revolutions because the geometric series converges.
