Linear Stability of Closed Timelike Geodesics

TL;DR

This paper investigates the linear stability of closed timelike geodesics and curves across various cylindrically symmetric spacetimes, including rotating dust cylinders, cosmic string configurations, G"odel-type universes, and specific Einstein-Maxwell solutions.

Contribution

It provides a comprehensive analysis of the existence and stability of closed timelike geodesics in multiple spacetime models with cylindrical symmetry.

Findings

Stability conditions for CTGs in rotating dust cylinders.

Existence criteria for CTGs in G"odel-type spacetimes.

Stability analysis of CTGs in Einstein-Maxwell solutions.

Abstract

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 G\"odel universe (G\"odel-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.