Surfaces de Cauchy polyédrales des espaces temps plats singuliers

Abstract : The study of singular flat spacetimes with polyhedral Cauchy-surfaces is motivated by the quantum gravity toy model role they play in the seminal work of Deser, Jackiw and 'T Hooft. This thesis study parametrisations of classes of singular flat spacetimes : Cauchy-compact maximal flat spacetimes with massive and BTZ-like singularities. Two parametrisations are constructed. The first is based on an extension of Mess theorem to flat spacetimes with BTZ and Penner-Epstein convex hull construction. The second is based on a generalisation of Alexandrov polyhedron theorem to radiant Cauchy-compact flat spacetimes with massive and BTZ-like singularities. This work also initiate a wider theoretical background that encompass singular spacetimes.
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Léo Brunswic. Surfaces de Cauchy polyédrales des espaces temps plats singuliers. Géométrie différentielle [math.DG]. Université d'Avignon, 2017. Français. ⟨NNT : 2017AVIG0420⟩. ⟨tel-01818016⟩

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