Discrete Group Actions on Spacetimes: Causality Conditions and the Causal Boundary

TL;DR

This paper explores how causality conditions and the causal boundary of a spacetime quotient relate to those of the original spacetime, providing insights into boundary structures via group actions.

Contribution

It establishes conditions under which causality and boundary properties are preserved or related in quotients of spacetimes by discrete isometry groups.

Findings

Causality conditions in the quotient spacetime relate to those in the original spacetime.

The boundary of the quotient spacetime can be understood as the quotient of the original boundary.

Simplifications occur when both spacetimes have spacelike future boundaries and certain automatic conditions are met.

Abstract

Suppose a spacetime $M$ is a quotient of a spacetime $V$ by a discrete group of isometries. It is shown how causality conditions in the two spacetimes are related, and how can one learn about the future causal boundary on $M$ by studying structures in $V$. The relations between the two are particularly simple (the boundary of the quotient is the quotient of the boundary) if both $V$ and $M$ have spacelike future boundaries and if it is known that the quotient of the future completion of $V$ is past-distinguishing. (That last assumption is automatic in the case of $M$ being multi-warped.)