Closed Geodesics on Godel-type Backgrounds

TL;DR

This paper investigates the behavior of supertube and string probes in Godel-type backgrounds, explicitly solving equations of motion and discovering closed geodesics, revealing new insights into probe dynamics in these spacetimes.

Contribution

It provides the first explicit solutions for probe trajectories, including closed geodesics, in Godel-type backgrounds derived from U-duality and Penrose limits.

Findings

Explicit solutions for probe equations of motion.

Identification of closed geodesics in Godel backgrounds.

Probes are not restricted to unidirectional travel.

Abstract

We consider radial oscillations of supertube probes in the Godel-type background which is U-dual to the compactified pp-wave obtained from the Penrose limit of the NS five-brane near horizon geometry. The supertube probe computation can be carried over directly to a string probe calculation on the U-dual background. The classical equations of motion are solved explicitly. In general, the probe is not restricted to travel unidirectionally through any global time coordinate. In particular, we find geodesics that close.