Linear Stability of Closed Timelike Geodesics

The linear stability of closed timelike geodesics (CTGs) is analyzed in two spacetimes with cylindrical sources, an infinite rotating dust cylinder, and a cylindrical cloud of static cosmic strings with a central spinning string. We also study the existence and linear stability of closed timelike curves in spacetimes that share some common features with the Gödel universe (Gödel-type spacetimes). In this case the existence of CTGs depends on the `background' metric. The CTGs in a subclass of inhomogeneous stationary cosmological solutions of the Einstein-Maxwell equations with topology $S^3\times \mathbb R$ are also examined.

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