Conformal transformations of spacetimes without observer horizons

TL;DR

This paper classifies conformal transformations in certain Lorentzian manifolds, particularly causal spacetimes without observer horizons, distinguishing between escaping and non-escaping types, and applies this to Einstein's static universe.

Contribution

It introduces a classification of conformal transformations for a class of Lorentzian manifolds and analyzes their properties, including essentiality and specific cases like Einstein's static universe.

Findings

Conformal transformations are either escaping or non-escaping in the studied spacetimes.

The classification applies to Einstein's static universe.

Some conformal transformations are isometric for certain metrics.

Abstract

We prove that for a certain class of Lorentzian manifolds, namely causal spacetimes without observer horizons, conformal transformations can be classified into two types: escaping and non-escaping. This means that successive powers of a given conformal transformation will either send all points to infinity, or none. As an application, we classify the conformal transformations of Einstein's static universe. We also study the question of essentiality in this context, i.e. which conformal transformations are isometric for some metric in the conformal class.