Stability of Closed Timelike Curves in Goedel Universe

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.

arXiv comment12 pages, 11 figures, RevTex, several typos corrected. GRG, in press

References in corpus (6)

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• Closed timelike curves and geodesics of Godel-type metrics
• Godel-Type Metrics in Various Dimensions
• Spinning cosmic strings: a general class of solutions
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Cited by in corpus (5)

• Relativistic cosmology and large-scale structure
• Spinning Strings, Black Holes and Stable Closed Timelike Geodesics
• Stability of Closed Timelike Geodesics
• Casimir force in the Gödel space-time and its possible induced cosmological inhomogeneity
• On Solutions to the Wave Equation on Non-globally Hyperbolic Manifold