Enveloping space of a globally hyperbolic conformally flat spacetime

2023/11/29 by Smaï, Rym · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2311.17802

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.

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