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Abstract: Closed timelike curves CTCs appear in many solutions of the Einsteinequation, even with reasonable matter sources. These solutions appear toviolate causality and so are considered problematic. Since CTCs reflect theglobal properties of a spacetime, one can attempt to change its topology,without changing its geometry, in such a way that the former CTCs are no longerclosed in the new spacetime. This procedure is informally known as unwrapping.However, changes in global identifications tend to lead to local effects, andunwrapping is no exception, as it introduces a special kind of singularity,called quasi-regular. This -unwrapping- singularity is similar to the stringsingularities. We give two examples of unwrapping of essentially 2+1dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. Weshow that the unwrapped Gott spacetime, while singular, is at least devoid ofCTCs. In contrast, the unwrapped Godel spacetime still contains CTCs throughevery point. A -multiple unwrapping- procedure is devised to remove theremaining circular CTCs. We conclude that, based on the two spacetimes weinvestigated, CTCs appearing in the solutions of the Einstein equation are notsimply a mathematical artifact of coordinate identifications, but are indeed anecessary consequence of General Relativity, provided only that we demand thesesolutions do not possess naked quasi-regular singularities.



Author: Sergei Slobodov

Source: https://arxiv.org/







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