Stability of Closed Timelike Curves in Goedel Universe

Details Stability of Closed Timelike Curves in Goedel Universe Stability of Closed Timelike Curves in Goedel Universe

2007-03-20

arxiv.org/abs/gr-qc/0703100v2

Gen.Rel.Grav.39:1419-1435,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1007/s10714-007-0464-9

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.

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