Musings

Gödel

The postdocs, Drukker, Fiol and Simon, here at Weizmann have put out a paper on a possible stringy resolution of the Gödel geometry.

String theory has a variety of mechanisms for resolving the pathologies of general relativity. The one most relevant here is the enhançon mechanism, in which a collection of D-branes puff out in the transverse directions, effectively excising the neighbourhood of the singularity, replacing it by a smooth interior geometry.

Drukker et al look at the Gödel universe with fluxes (a configuration of type IIA preserving 8 supercharges)

where $A=- c r^2 d\phi$. For $r\gt 1/c$, this geometry has closed timelike curves (the circles $\phi\in [0,\pi]$, with the other coordinates constant are spacelike for $r\lt 1/c$, but timelike for $r\gt 1/c$.

In a sort of inside-out version of the enhançon, they argue that there’s a supertube configuration whose interior geometry is Gödel, but whose exterior is smooth, with no CTC’s.

Now, the nice thing about the enhançon is that it’s a local effect. If you had some physical process which would lead to a repulson singularity, you expect the nucleation of some D-branes which would pop out from the origin and repair the singularity. This is a local process; the asymptotic behaviour of the metric is unchanged.

In the Gödel geometry, it is the asymptotic region that is bad. Drukker et al’s supertubes nucleate, as it were, at infinity, and come in to repair the metric. Normally, we would reject such a scenario as bananas. It requires a nonlocal conspiracy of the quantum fields at arbitrarily large separations. On the other hand, this region of the Gödel geometry has closed timelike curves, so there is infinite scope for such a conspiracy to assemble itself. Maybe not so bananas …

I don’t want to advocate this picture too literally. The physical question is whether there is some initial configuration which would, in GR, evolve into a geometry with closed timelike curves and whether it is saved from this fate in string theory. The Gödel geometry does not address the former question, so any “resolution” of Gödel does not address the latter.