The discussion centers on the existence of Closed Timelike Curves (CTC) in Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models. It is established that FLRW models, characterized by their topology of either ##\mathbb R^4## or ##\mathbb S^3 \times \mathbb R##, do not permit CTCs as cosmological time ##t## consistently increases along future-directed timelike curves. Examples of metrics that do exhibit CTCs include the Kerr interior, Gödel metric, and Tipler cylinder; however, these are not considered plausible cosmological models. The consensus is that metrics used for actual physical systems are globally hyperbolic and thus cannot contain CTCs.
PREREQUISITESPhysicists, cosmologists, and students of general relativity who are interested in the implications of time travel in theoretical models and the characteristics of spacetime metrics.
Ah ok. Which are examples of spacetime metric that have CTC? Are they a reasonable cosmological model ?Orodruin said:No. The cosmological time ##t## always increases along future-directed timelike curves.
No metrics that are used for modeling actual physical systems have CTCs. All such metrics are globally hyperbolic, and a globally hyperbolic spacetime cannot have any CTCs. (Indeed, even spacetimes satisfying much weaker conditions cannot have any CTCs. The full gory details are in Hawking & Ellis.)cianfa72 said:Do they have any CTC ?
Does that mean we don't regard the Kerr metric as plausible? Or just the bit near the ring singularity where CTCs exist?PeterDonis said:No metrics that are used for modeling actual physical systems have CTCs.
Yes, the CTCs in Kerr are only inside the inner horizon, and since the inner horizon is a Cauchy horizon, even if one has a spacetime that one knows to be Kerr everywhere outside the inner horizon, one cannot claim that it is Kerr inside the inner horizon. The general view among relativity physicists seems to be that the actual interior of a rotating black hole will not even contain a Kerr inner horizon, but will have some other structure that, causally speaking, looks more like Schwarzschild.Ibix said:Does that mean we don't regard the Kerr metric as plausible? Or just the bit near the ring singularity where CTCs exist?