Globally hyperbolic conformally flat spacetimes
type: Dataset
description: As a consequence of the Lorentzian version of Liouville’s Theorem, everyconformally flat space-time of dimension 3 is a (Ein1,n,O0(2, n + 1))-manifold. The Einstein’s space-time Ein1,n is the space Sn × S1 with theconformal class of the metric d2−dt2, where d2 and dt2 are the canonicalRiemannian metrics of Sn and R. The group O0(2, n+1) is the group of theconformal diffeomorphisms of Ein1,n whose action preserve the orientationand the time-orientation of Ein1,n. A space-time M is globally hyperbolicif it contains a spacelike hypersurface which intersects every inextensiblecausal curve of M exactly in one point. As a consequence M is not compact.The hypersurface is called a Cauchy hypersurface of M. Geroch’s Theorem([?]) say that if M is globally hyperbolic, then M is homeomorphic to×R. There is a naturally defined partial order on the set of globally hyperbolicspace-times (up to conformal diffeomorphism) : M M0 if does existsa conformal embedding f : M ,! M0 which sends Cauchy hypersurfaces ofM to Cauchy hypersurfaces of M0 (f is called a Cauchy-embedding ). Wecall C-maximal space-times the maximal elements for this partial order onthe set of globally hyperbolic space-times. We can restrict the partial orderto the subset of conformally flat space-times : in this case we call themaximal elements C0-maximal space-times. The first result of the thesis isa generalization of a Theorem proved by Choquet-Bruhat and Geroch in[?] : let M be a globally hyperbolic conformally flat space-time. Then thereis a globally hyperbolic conformally flat C0-maximal space-time N and aCauchy-embedding f : M ,! N. The space-time N is unique up to conformaldiffeomorphisms.The uniqueness of the C0-maximal extension imply that every globally hyperbolicconformally flat simply connected C0-maximal space-time (of dimension3) with a compact Cauchy hypersurface is conformally diffeomorphicto gEin1,n.In the second part of the thesis we study the injectivity of the developingmap of a globally hyperbo…
identifier: NNT: 2012AVIG0408
issued: 2026-05-07T07:29:02.414596
language: fr
modified: 2026-05-07T07:29:02.414602
contact point: Organization
  fn: CCSD
keyword: causalite
keyword: causality
keyword: conformal-geometry
keyword: differential-geometry
keyword: einstein-equation
keyword: equation-deinstein
keyword: espace-temps
keyword: geometrie-conforme
keyword: geometrie-differentielle
keyword: geometrie-lorentzienne
keyword: globally-hyperbolic-manifolds
keyword: gx-structures
keyword: gx-structures-on-manifolds
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lorentzian-geometry
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: space-times
keyword: theses
keyword: variete-globalement-hyperboliques
landing page: https://theses.hal.science/tel-00934781

Globally hyperbolic conformally flat spacetimes
type: Distribution
format: HTML
issued: 2026-05-07T07:29:02.429162
modified: 2026-05-07T07:29:02.396912
access URL: https://theses.hal.science/tel-00934781

test_moissonnage_selune
type: Agent