Causal inheritance in plane wave quotients

TL;DR

This paper analyzes when quotients of plane wave spacetimes develop closed timelike curves, establishing conditions for stable causality and classifying quotients based on their isometries.

Contribution

It provides a necessary and sufficient condition for stable causality in spacetime quotients and classifies all quotients of the maximally supersymmetric plane wave.

Findings

Plane waves are generally stably causal.

Quotients involving translation along the u direction produce closed timelike curves.

Other quotients preserve stable causality.

Abstract

We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp-waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave spacetimes. We show that all other quotients preserve stable causality.