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Träfflista för sökning "WFRF:(Isenberg James Professor) "

Sökning: WFRF:(Isenberg James Professor)

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1.
  • Radermacher, Katharina Maria, 1987- (författare)
  • Strong Cosmic Censorship and Cosmic No-Hair in spacetimes with symmetries
  • 2017
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity.In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids.In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry.
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2.
  • Sakovich, Anna (författare)
  • A study of asymptotically hyperbolic manifolds in mathematical relativity
  • 2012
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis consists of ve papers where certain problems arising in mathematical relativity are studied in the context of asymptotically hyperbolic manifolds.In Paper A we deal with constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds. Conditions on the scalar field and its potential are given which lead to existence and non-existence results.In Paper B we construct non-constant mean curvature solutions of the constraint equations on asymptotically hyperbolic manifolds. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then letting the exponent tend to its true value. We prove that if a certain limit equation admits no non-trivial solution, then the set of solutions of the constraint equations is non empty and compact. W ealso give conditions ensuring that the limit equation admits no nontrivial solution. This is a joint work with Romain Gicquaud.In this Paper C we obtain Penrose type inequalities for asymptotically hyperbolic graphs. In certain cases we prove that equality is attained only by the anti-de Sitter Schwarzschild metric. This is a joint work with Mattias Dahl and Romain Gicquaud.In Paper D we construct a solution to the Jang equation on an asymptotically hyperbolic manifold with a certain asymptotic behaviour at infinity.In Paper E we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that when the mass tends to zero the metric converges uniformly tot he hyperbolic metric. This is a joint work with Mattias Dahl and Romain Gicquaud.
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