Gott time machines in the Anti-de Sitter space

TL;DR

This paper explores the existence of closed timelike curves in Anti-de Sitter space, extending Gott's 1991 solution from flat spacetime to negatively curved space, and demonstrates these curves remain tachyonic.

Contribution

It generalizes Gott's construction of closed timelike curves to Anti-de Sitter space with negative cosmological constant, analyzing their properties and tachyonic nature.

Findings

CTCs can be constructed in Anti-de Sitter space similarly to flat space.

Such CTCs in AdS are also tachyonic.

The paper provides insights into the structure of AdS space relevant to CTCs.

Abstract

In 1991 Gott presented a solution of Einstein's field equations in 2+1 dimensions with $\Lambda = 0$ that contained closed timelike curves (CTC's). This solution was remarkable because at first it did not seem to be unphysical in any other respect. Later, however, it was shown that Gott's solution is tachyonic in a certain sense. Here the case $\Lambda < 0$ is discussed. We show that it is possible to construct CTC's also in this case, in a way analogous to that used by Gott. We also show that this construction still is tachyonic. $\Lambda < 0$ means that we are dealing with Anti-de Sitter space, and since the CTC-construction necessitates some understanding of its structure, a few pages are devoted to this subject.