Unwrapping Closed Timelike Curves

TL;DR

This paper investigates the process of unwrapping closed timelike curves in certain spacetimes, revealing that CTCs are not just coordinate artifacts but inherent in some solutions of Einstein's equations, with implications for causality in general relativity.

Contribution

The paper demonstrates how unwrapping CTCs affects spacetime topology and singularities, providing specific examples with Gott and Godel spacetimes, and introduces a multiple unwrapping method.

Findings

Unwrapping can remove CTCs in some spacetimes like Gott.

Unwrapping may introduce quasi-regular singularities.

Some spacetimes, like Godel, retain CTCs even after unwrapping.

Abstract

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 change its topology, without changing its geometry, in such a way that the former CTCs are no longer closed in the new spacetime. This 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 give two examples of unwrapping of essentially 2+1 dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We show that the unwrapped Gott spacetime, while singular, is at least devoid of CTCs. In contrast, the unwrapped Godel 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 two spacetimes we investigated, CTCs appearing in the solutions of the Einstein equation are not simply a mathematical artifact of coordinate identifications, but are indeed a necessary consequence of General Relativity, provided only that we demand these solutions do not possess naked quasi-regular singularities.