Globally hyperbolic spatially compact maximal conformally flat spacetimes arising from Anosov representations
Rym Smaï1
1 Laboratoire J. A. Dieudonné Université Côte d’Azur 06000 Nice (France)
Séminaire de théorie spectrale et géométrie, Tome 37 (2021-2022), pp. 137-175.

This paper deals with Anosov representations of a Gromov-hyperbolic group into the semi-simple Lie group O 0 (2,n) and their link with conformally flat Lorentzian structures on manifolds. The main result that we discuss states that any P 1 -Anosov representation of a Gromov hyperbolic group into O 0 (2,n) preserving an acausal subset in the Einstein universe Ein 1,n-1 is the holonomy of a globally hyperbolic Cauchy-compact maximal conformally flat spacetime. It follows from this result remarkable examples, that we call black-white holes, conformally flat Misner spacetimes and Misner extensions and that we describe in this paper. Last but not least, we introduce and we discuss the notion of complete photons that appears naturally in these examples.

Publié le :
DOI : 10.5802/tsg.385

Rym Smaï 1

1 Laboratoire J. A. Dieudonné Université Côte d’Azur 06000 Nice (France) 
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Rym Smaï. Globally hyperbolic spatially compact maximal conformally flat spacetimes arising from Anosov representations. Séminaire de théorie spectrale et géométrie, Tome 37 (2021-2022), pp. 137-175. doi : 10.5802/tsg.385. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.385/

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