Chronology protection in stationary 3D spacetimes

TL;DR

This paper investigates the conditions under which closed timelike curves can exist in stationary 2+1 dimensional spacetimes with negative cosmological constant, showing they are linked to boundary causality issues or unphysical matter content.

Contribution

It classifies stationary 3D spacetimes with closed timelike curves into two categories based on boundary causality and matter energy conditions, providing a framework for understanding chronology protection.

Findings

Closed timelike curves imply bad asymptotics or unphysical stress tensors.

Examples involve rotating dust in anti-de Sitter space.

AdS/CFT correspondence offers insights into chronology protection.

Abstract

We address chronology protection in stationary, rotationally symmetric spacetimes in 2+1 dimensional gravity, focusing on the case of negative cosmological constant. We show that, if such spacetimes contain closed timelike curves, they belong to one of the following two classes: (i) bad asymptotics: the boundary itself contains closed timelike curves, or (ii) unphysical stress tensor in the bulk: the matter stress tensor violates the null energy condition. 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.