On the conformal group of a globally hyperbolic spacetime

TL;DR

This paper investigates the structure of conformal groups in globally hyperbolic spacetimes, establishing classification results in two dimensions and extending to locally conformally flat cases, enhancing understanding of spacetime symmetries.

Contribution

It provides a classification of causal and conformal automorphism groups in two-dimensional globally hyperbolic spacetimes and generalizes results to locally conformally flat cases.

Findings

All directed, connected globally hyperbolic spacetimes in 2D are causally isomorphic.

Classification of conformal automorphism groups in 2D globally hyperbolic spacetimes.

Extension of classification results to locally conformally flat globally hyperbolic spacetimes.

Abstract

The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the consequences of this fact and obtain a (partial) classification of the causal automorphism and conformal groups of a two-dimensional globally hyperbolic space. Finally, we present a generalization for locally conformally flat globally hyperbolic spacetimes.