Foundations of Physics

, 38:1082 | Cite as

Unwrapping Closed Timelike Curves



Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of a spacetime, one can attempt to extend a local CTC-free patch of such a spacetime in a way that does not give rise to CTCs. One such procedure is informally known as unwrapping. However, changes in global identifications tend to lead to local effects, and unwrapping is no exception, as it introduces a special kind of singularity, called quasi-regular. This “unwrapping” singularity is similar to the string singularities. We define an unwrapping of a (locally) axisymmetric spacetime as the universal cover of the spacetime after one or more of the local axes of symmetry is removed. We give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Gödel spacetime. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Gödel spacetime still contains CTCs through every point. A “multiple unwrapping” procedure is devised to remove the remaining circular CTCs. We conclude that, based on the given examples, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications. Alternative extensions of spacetimes with CTCs tend to lead to other pathologies, such as naked quasi-regular singularities.


Closed timelike curves Gödel universe Gott spacetime 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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