# "Realistic" CTC formation in GR

1. Oct 5, 2015

### tzimie

I know there are solutions with CTC, I know about:

1. Goedel Universe
2. Case with moving infinite sticks
3. Ring singularity inside the rotating BH

However, in all 3 cases above CTC is "eternal" - the universe "always" contains CTC, and case 3 is a part of the "eternal" BH, We know "realistic" BH are quite different, for example, there is no corresponding "white hole" part of the solution.

So my question is, can we create CTC from nothing - having initially Universe without CTC and without high curvature (so notion of "global time" can be used in some sense, and we can say "at some TIME there were no CTCs) but trajectories of ideal dust are adjusted in a way that CTC is created somewhere at SOMETIME?

Or are CTC always "eternal" and can't be created in any realistic scenario?

And related question, depending on the answer above, does *realistic* Kerr BH have ring singularities inside?

P.S.
I know that QFT diverges near the CTC and (probably) prevents their formation, but my question is about "pure" GR.

2. Oct 5, 2015

### Ben Niehoff

Fairly sure the time-dependent scenario of stellar collapse which forms a Kerr black hole gives you what you're looking for. But the CTCs are all behind the horizon.

3. Oct 5, 2015

### tzimie

Wait. If there is matter, "orbiting" in a circular worldline in CTC, then you can't track this worldline "back in time" to some earlier state. For example, if you take Uranium atom in a stellar cloud, you can track it back to the origin (likely, supernova explosion). Matter inside CTC, however, does not have an "origin". So, if matter infalling into BH comes from the outside, how the matter inside CTC gets there in the first place?

As an another attempt to show my confusion. Say, I have a powerful computer to simulate dust particles based on laws of GR. Usually simulations use small steps in time one by one. In GR it is problematic as time itself is curved, but still it is complicated but possible. So, I put any dust configuration into that simulator and I check how system evolves. Now say CTC forms in the simulation. But CTC region is not causally connected with the past, with the rest of the previous simulation. So you can't, in principle, derive what is inside CTC based on the initial conditions in the past! I can say that it is pink unicorn orbiting in CTC, and if mass and momentum of the unicorn is consistent with the solution - it is possible!

4. Oct 5, 2015

### Ben Niehoff

Yes, CTCs present problems for time evolution. CTCs are always in some region of space whose boundary is known as a "Cauchy horizon". This means that the Cauchy problem (i.e., the initial value problem, or time evolution) becomes ill-defined as you cross into a region of CTCs. You can think of a Cauchy horizon as marking the boundary of a "Here be dragons" region of spacetime.

5. Oct 5, 2015

### tzimie

So because of Cauchy problem even almost universal bare-force numerical methods fail to calculate what is inside a realistic rotating BH?

6. Oct 5, 2015

### bcrowell

Staff Emeritus
What you're referring to is called the chronology protection conjecture https://en.wikipedia.org/wiki/Chronology_protection_conjecture , and AFAIK it's still an open problem. Both chronology protection and cosmic censorship are problems where the difficulty may be as much in finding the proper formulation of the conjecture as in proving it. It would actually be really nice to find a recent review article on the CPC. I just don't know of one.

If you have a traversable wormhole, then there are generic arguments that you can use it to create CTCs. So if it were possible to form a traversable wormhole starting from a universe that didn't have one, you would probably automatically have a violation of the CPC. But there are theorems that prove you can't do this without exotic matter; see Borde, 1994, "Topology Change in Classical General Relativity," http://arxiv.org/abs/gr-qc/9406053 .

Since the Kerr metric dates back to 1963, while the CPC is an open problem, it seems to me that there must be a problem with this. The Kerr solution is an eternal black hole, and its interior is unstable. This instability makes it seem unlikely to me that an object whose interior has the structure of a Kerr black hole can form by gravitational collapse.