I CTC on FLRW cosmological models

[cianfa72]

TL;DR Summary

About the existence of CTC in FLRW models

The subject of this thread is about the existence of Closed Timelike Curves (CTC) in FLRW models. FLRW models have topology $\mathbb R^4$ or $\mathbb S^3 \times \mathbb R$.

What about their metric? Do they have any CTC ?

 

[Orodruin]

No. The cosmological time $t$ always increases along future-directed timelike curves.

 

[cianfa72]

No. The cosmological time $t$ always increases along future-directed timelike curves.

Ah ok. Which are examples of spacetime metric that have CTC? Are they a reasonable cosmological model ?

 

[Ibix]

Kerr interior. Gödel. Tipler cylinder. There are probably others. None of them that I'm aware of are plausible cosmological spacetimes.

 

[PeterDonis]

Do they have any CTC ?

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.)

 

[Ibix]

No metrics that are used for modeling actual physical systems have CTCs.

Does that mean we don't regard the Kerr metric as plausible? Or just the bit near the ring singularity where CTCs exist?

 

[PeterDonis]

Does that mean we don't regard the Kerr metric as plausible? Or just the bit near the ring singularity where CTCs exist?

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.