CTCs in Kerr Metric: Examining the Invariance of CTCs in Spacetime

[yuiop]

Are CTCs in the Kerr metric just an artefact of the coordinates used?

This paper http://arxiv.org/abs/gr-qc/0207014 suggests that is the case. In a private message it has been suggested to me that CTCs in a spacetime are an invariant feature so are not removable by a change of coordinate system (unlike the event horizon in the Schwarzschild metric). If that is the case, can anyone pinpoint where the argument of the authors of the paper is flawed?

 

[PAllen]

A curve being closed, and being timelike, are definitely invariant features that cannot be removed by coordinate transforms. If the authors succeed (as they claim) in showing there are no CTC's near the ring singularity, they would need to explain the discrepancy more than they do - the claim that that this can be an coordinate artifact is absurd on its face.

Unfortunately, I don't have time to try pinpoint the specific error(s) of this paper. [Even if they were right that there are no CTCs, the paper is still in error in how it presents this - it cannot be a coordinate artifact, thus they need to explain the error in other people's analysis in a valid way].

 

[K^2]

Yes. Whether or not any infinitesimal path element is time-like or not is completely coordinate-independent. A CTC in one coordinate system is a CTC in every coordinate system. If the author gets something that's not time-like in a different coordinate system, then the mistake is either in his approach, or the path is not a CTC in Kerr-Newman either. Since proof of CTC in Kerr-Newman is very straightforward and pretty fool-proof, I would bet on the paper being wrong.

 

[yuiop]

If we consider a rotating ring in flat spacetime and syncronise clocks attached to the ring using the Einstein synchronisation convention, (so that observers riding on the ring measure the speed of light to be same in either direction along the ring), then we end up with an ambiguous definition of coordinate time around the ring for distances greater than the circumference. Using such a coordinate system could result in apparent CTCs where a particle traveling around the ring arrives back at its initial starting point on the ring at the same coordinate time. Obviously this would be a really *bad* coordinate system to use on the ring and causes artefacts and ambiguities.

I am wondering if something similar is going wrong in the the proposed alternative coordinate system or in the Kerr metric itself. In a rotating system, a good coordinate system has non-isotropic one way speed of light locally and a bad coordinate system has an isotropic one way speed of light locally.

 

[PAllen]

If we consider a rotating ring in flat spacetime and syncronise clocks attached to the ring using the Einstein synchronisation convention, (so that observers riding on the ring measure the speed of light to be same in either direction along the ring), then we end up with an ambiguous definition of coordinate time around the ring for distances greater than the circumference. Using such a coordinate system could result in apparent CTCs where a particle traveling around the ring arrives back at its initial starting point on the ring at the same coordinate time. Obviously this would be a really *bad* coordinate system to use on the ring and causes artefacts and ambiguities.

I am wondering if something similar is going wrong in the the proposed alternative coordinate system or in the Kerr metric itself. In a rotating system, a good coordinate system has non-isotropic one way speed of light locally and a bad coordinate system has an isotropic one way speed of light locally.

That's all irrelevant. The only way for a curve to be closed in one coordinate system and not in another is if the mapping is not one-one, thus not a valid coordinate transform. Further, the timelike/spacelike character of every tangent vector is invariant. The paper claim (that CTC can be a coordinate effect) is just absurd.

 

[yuiop]

That's all irrelevant. The only way for a curve to be closed in one coordinate system and not in another is if the mapping is not one-one, thus not a valid coordinate transform. ..

Well that is sort of the point of my last post. They use a new time coordinate $\tilde{t} = t +(a \sin^2\phi)\theta_0$ which is dependent on $\theta$ and potentially has a cyclic ambiguity that does not allow a unique one to one mapping to the new coordinate system.

 

[PAllen]

Well that is sort of the point of my last post. They use a new time coordinate $\tilde{t} = t +(a \sin^2\phi)\theta$ which is dependent on $\theta$ and potentially has a cyclic ambiguity that does not allow a unique one to one mapping to the new coordinate system.

If they do that, without dealing with the closure issue, that is really dumb. Circles in the plane are not closed anyone? I hope the mistake is not as trivial as that, but you could be right.