What is the interpretation of a Misner string in Bonnor's theory?

[bcrowell]

I came across the term "Misner string" in this paper: http://arxiv.org/abs/1509.07854

My understanding is that this originated in the study of spacetimes such as Taub-NUT. If I'm understanding correctly, this involves CTCs encircling the string. Misner's original interpretation of the string was that time was forced to be periodic, which caused energy to be quantized; this makes the string unobservable. Bonnor proposed instead to treat Misner string as a topological defect, with matter as a source: Bonnor, Proc Camb Phil Soc 66 (1969) 145 http://journals.cambridge.org/actio...587332E4.journals?fromPage=online&aid=2067080 . Unfortunately the old papers seem to be paywalled, so I can't access them. (As usual, the journals are doing their best imitations of Mordac, Preventer of Information Services.)

Does anyone know of any freely available description of this topic?

 

[S.G. Janssens]

I found a search on Google Scholar for "A new interpretation of the NUT metric in general relativity" to be very revealing.

 

[martinbn]

Is it this one?

 

[bcrowell]

@martinbn: Thank you for posting that. It's very helpful to me. But although I know you're trying to be helpful, I think it would have been better to post it somewhere else. PF has a rule against posting copyrighted materials, and I think we should respect that.

Personally, I feel that the copyright regime in my country (the US) is unjust, and I often do violate it by posting papers online. However, I don't think PF is the right place to do it.

 

[martinbn]

I didn't even think about that. Doesn't it fit the fair use criteria? Anyway, I cannot edit my post, can someone with the ability to edit delete my post.

 

[bcrowell]

I didn't even think about that. Doesn't it fit the fair use criteria? Anyway, I cannot edit my post, can someone with the ability to edit delete my post.

I'm a strong supporter of fair use, and you're right, this probably does fall under fair use in the US. But the criteria for fair use are very vague, so the only way you can ever know for sure whether something is fair use is to get sued and find out whether you win the lawsuit. In this case it would theoretically be Greg who would get sued.

 

[bcrowell]

So using my illicitly gained knowledge, here's a summary of what I think a Misner string is.

In Bonnor's interpretation, it's a "semi-infinite massless source of angular momentum," i.e., half a line reaching out to infinity from some central point. It has a parameter, called the NUT parameter, which in this interpretation equals half the angular momentum per unit length. Geometrically, I think it's some sort of topological defect, and I think it's also a singularity (there's geodesic incompleteness), but not a curvature singularity.

The interpretation is a little subtle, because the spacetime isn't asymptotically flat, and therefore we can't define things like mass and angular momentum from the point of view of an observer at infinity. Bonnor gets around this by using a linearized approximation to GR in which he can extract certain multipole moments.

Bonnor arbitrarily cuts out all the badly behaved pieces of the spacetime, which I think means that it's less than a maximal extension. He says that it should be possible to fill these holes back in with some better-behaved pieces, but he doesn't do it in this paper. I think this is what Hawking and Ellis do in their treatment, and that seems to get complicated, with issues such as non-Hausdorff behavior.

Bonnor's interpretation is different from Misner's original interpretation. Misner apparently embraces the CTCs rather than excising them, and makes the string go away. (I haven't seen his actual paper.) Misner was apparently influenced by the Killing vectors of the spacetime, which show it to be homogeneous. If it's homogeneous, then it seems intuitively that it can't have a feature such as a physical string sticking out of it. But Bonnor argues that the Killing vector misbehaves where the string is, so we can get a homogeneous field from an inhomogeneous source. He makes a nice Newtonian analogy with the field of a sheet of mass, which is homogeneous.