Chronology protection in stationary three-dimensional spacetimes

TL;DR

This paper investigates the conditions under which closed timelike curves can exist in stationary, rotationally symmetric 2+1 dimensional spacetimes with negative cosmological constant, linking bulk matter properties to boundary conformal weights.

Contribution

It demonstrates that closed timelike curves require either boundary existence or null energy condition violation in the bulk, and connects bulk matter to dual CFT conformal weights.

Findings

Closed timelike curves extend to the boundary or violate null energy condition.

Matter in CTC regions contributes negatively to the dual CFT conformal weight.

Examples involve rotating dust in anti-de Sitter space.

Abstract

We study chronology protection in stationary, rotationally symmetric spacetimes in 2+1 dimensional gravity, focusing especially on the case of negative cosmological constant. We show that in such spacetimes closed timelike curves must either exist all the way to the boundary or, alternatively, the matter stress tensor must violate the null energy condition in the bulk. We also show that the matter in the closed timelike curve region gives a negative contribution to the conformal weight from the point of view of the dual conformal field theory. We illustrate these properties in a class of examples involving rotating dust in anti-de Sitter space, and comment on the use of the AdS/CFT correspondence to study chronology protection.