Enveloping space of a globally hyperbolic conformally flat spacetime

TL;DR

This paper proves that any simply-connected globally hyperbolic conformally flat spacetime can be embedded into a larger conformally flat spacetime called its enveloping space, which contains all conformally flat Cauchy-extensions, ensuring existence and uniqueness of maximal extensions.

Contribution

It introduces the concept of an enveloping space for such spacetimes and provides a new proof for the existence and uniqueness of C0-maximal extensions.

Findings

Existence of an enveloping space containing all conformally flat Cauchy-extensions.

Uniqueness of the C0-maximal extension of a globally hyperbolic conformally flat spacetime.

Extensions respect inclusion, preserving the structure of the spacetime hierarchy.

Abstract

We prove that any simply-connected globally hyperbolic conformally flat spacetime V can be conformally embedded in a bigger conformally flat spacetime, called enveloping space of V , containing all the conformally flat Cauchy-extensions of V , in particular its C 0-maximal extension. As a result, we establish a new proof of the existence and the uniqueness of the C 0-maximal extension of a globally hyperbolic conformally flat spacetime. Furthermore, this approach allows us to prove that C 0-maximal extensions respect inclusion.