Causal and conformal structures of globally hyperbolic spacetimes

TL;DR

This paper characterizes the conformal and causal automorphism groups of two-dimensional globally hyperbolic spacetimes, showing they are subgroups of Minkowski or Einstein's static universe depending on the Cauchy surface topology.

Contribution

It provides a detailed classification of automorphism groups based on the topology of Cauchy surfaces in 2D globally hyperbolic spacetimes.

Findings

Groups are subgroups of Minkowski spacetime automorphisms for non-compact Cauchy surfaces.

Groups are subgroups of Einstein's static universe automorphisms for compact Cauchy surfaces.

Clarifies the structure of conformal and causal automorphisms in 2D globally hyperbolic spacetimes.

Abstract

The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if spacetimes have compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Einstein's static universe.