Goedel's Universe in a Supertube Shroud

TL;DR

The paper addresses whether Gödel-like rotating universes in supergravity can be realized as consistent string theory backgrounds. It employs BPS supertube probes to reveal a universal instability: worldvolume modes acquire negative kinetic terms when the radius satisfies $r \ge 1/c$, indicating the background cannot be a valid string vacuum. To manage the pathology, it constructs domain-wall solutions that are Gödel-like near the origin but asymptote to non-CTC spacetimes using harmonic functions $U$ and $V$ and Israel matching, showing CTCs can be avoided up to a regulator shell with $R \le 1/c$. The results argue that full Gödel limits ($R \to \infty$) cannot be realized as string backgrounds and suggest a general mechanism, akin to the enhançon, that eliminates broad classes of Gödel-type backgrounds with closed timelike curves from string theory.

Abstract

We demonstrate that certain supersymmetric Goedel-like universe solutions of supergravity are not solutions of string theory. This is achieved by realizing that supertubes are BPS states in these spaces, and under certain conditions, when wrapping closed timelike curves, some world-volume modes develop negative kinetic terms. Since these universes are homogeneous, this instability takes place everywhere in space-time. We also construct a family of supergravity solutions which locally look like the Goedel universe inside a domain wall made out of supertubes, but have very different asymptotic structure. One can adjust the volume inside the domain wall so there will be no closed timelike curves, and then those spaces seem like perfectly good string backgrounds.