# Frame dragging = CTC?

1. Jul 30, 2011

### Imax

Can frame dragging around a black hole induce closed timelike curves (CTC)?

2. Jul 30, 2011

### stevebd1

3. Jul 30, 2011

### Imax

4. Jul 31, 2011

### Chalnoth

Short answer: no. It would require a black hole rotating so fast that the horizon is eliminated, which can't happen.

5. Aug 1, 2011

### Imax

I'm just speculating about the possibility of a CTC outside the event horizon. What could a distant observer see?

Within a CTC, causality is lost. Cause and effect do not necessarily follow. A test particle can undergo a colision, but the effects of that colision could be seen in the past, before the colision happened.

The effects of any CTC within the event horizon of a black hole is not observable to a distant observer, but a CTC outside the event horizon should have some observable characteristics.

6. Aug 1, 2011

### Chalnoth

I know. It can't be done.

7. Aug 2, 2011

### Imax

Last edited: Aug 2, 2011
8. Aug 2, 2011

### Chalnoth

That, um, has no relevance to my point. There still aren't any closed time-like curves near the outside of the event horizon of a black hole, rotating or no.

9. Aug 3, 2011

### Imax

Sorry. I don’t mean to imply that there are CTCs outside the event horizon, but frame dragging seems to be generally associated with CTCs and there seems to be very few examples of metrics which:

1) have CTCs, and
2) are generally accepted as being physically meaningful (i.e. excluding ones like the Gödel metric).

In many metrics with CTCs, such as those with frame dragging, the CTCs seem to be hidden behind a horizon. Is this a general property of these types of metrics (i.e. CTCs are hidden behind a horizon) or are there assumptions made in constructing physically meaningful manifolds that makes this necessarily the case?

For example, if you what time to go from –infinity to +infinity, then you need to construct a manifold with two properties:

1) Time orientability
2) Global hyperbolicity

Do these properties make it so that CTCs are necessarily hidden behind horizons? Global hyperbolicity implies that there are no possible CTCs (but they sometimes creep in, like in the Kerr metric).

10. Aug 3, 2011

### Chalnoth

I believe this is the case, yes.