Stability of Closed Timelike Curves in Goedel Universe

TL;DR

This paper investigates the linear stability of closed timelike curves in the Goedel universe, demonstrating their stability even with matter inclusion, and explores conditions for matter that satisfy energy conditions.

Contribution

It provides a detailed analysis of the stability of closed timelike curves in the Goedel metric, including extensions with matter and stability under perturbations.

Findings

Closed timelike curves in Goedel universe are linearly stable.

Stability persists with both regular and exotic matter.

Structural stability of these curves is also established.

Abstract

We study, in some detail, the linear stability of closed timelike curves in the Goedel metric. We show that these curves are stable. We present a simple extension (deformation) of the Goedel metric that contains a class of closed timelike curves similar to the ones associated to the original Goedel metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in Goedel universe with or whithout the inclusion of regular or exotic matter are also stable under linear perturbations. We also find a sort of structural stability.