Enveloping space of globally hyperbolic conformally flat spacetimes
[Espace enveloppant des espace-temps globalement hyperboliques conformément plats]
Smaï, Rym1
1IRMA, 7 Rue René Descartes, 67000 Strasbourg (France)
Annales de l'Institut Fourier, Online first, 41 p.

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 $\mathcal{C}_0$-maximal extension. As a result, we establish a new proof of the existence and the uniqueness of the $\mathcal{C}_0$-maximal extension of a globally hyperbolic conformally flat spacetime. Furthermore, this approach allows us to prove that $\mathcal{C}_0$-maximal extensions respect inclusion.

Nous prouvons que tout espace-temps conformément plat globalement hyperbolique simplement connexe $V$ peut-être plongé conformément dans un espace-temps conformément plat plus grand, appelé espace enveloppant de $V$, qui contient toutes les extensions de Cauchy conformément plates de $V$, en particulier son extension $\mathcal{C}_0$-maximale. Il en découle une nouvelle preuve de l’existence et de l’unicité de l’extension $\mathcal{C}_0$-maximale d’un espace-temps conformément plat globalement hyperbolique. En outre, cette approche nous permet de montrer que les extensions $\mathcal{C}_0$-maximales respectent l’inclusion.

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Révisé le :
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Première publication :
DOI : 10.5802/aif.3758
Classification : 53C50
Keywords: spacetimes, global hyperbolicity, conformally flat, Cauchy extensions, maximality, enveloping space
Mots-clés : espace-temps, hyperbolicité globale, conformément plat, extensions de Cauchy, maximalité, espace enveloppant

Smaï, Rym  1

1 IRMA, 7 Rue René Descartes, 67000 Strasbourg (France) 
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Smaï, Rym. Enveloping space of globally hyperbolic conformally flat spacetimes. Annales de l'Institut Fourier, Online first, 41 p.

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