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Träfflista för sökning "WFRF:(Ringström Hans 1972 ) "

Sökning: WFRF:(Ringström Hans 1972 )

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2.
  • Radermacher, Katharina Maria, 1987- (författare)
  • Strong Cosmic Censorship and Cosmic No-Hair in spacetimes with symmetries
  • 2017
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • <p>Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori.</p><p>I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider.</p><p>I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri.</p>
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3.
  • Ringström, Hans, 1972- (författare)
  • A Unified Approach to the Klein-Gordon Equation on Bianchi Backgrounds
  • 2019
  • Ingår i: Communications in Mathematical Physics. - SPRINGER. - 0010-3616 .- 1432-0916. ; 372:2, s. 599-656
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>In this paper, we study solutions to the Klein-Gordon equation on Bianchi backgrounds. In particular, we are interested in the asymptotic behaviour of solutions in the direction of silent singularities. The main conclusion is that, for a given solution u to the Klein-Gordon equation, there are smooth functions u(i), i = 0, 1, on the Lie group under consideration, such that u(sigma) (. , sigma) - u(1) and u(. , sigma) - u(1)sigma - u(0) asymptotically converge to zero in the direction of the singularity (where s is a geometrically defined time coordinate such that the singularity corresponds to sigma -&gt; -infinity). Here u(i), i = 0, 1, should be thought of as data on the singularity. Interestingly, it is possible to prove that the asymptotics are of this form for a large class of Bianchi spacetimes. Moreover, the conclusion applies for singularities that arematter dominated; singularities that are vacuum dominated; and even when the asymptotics of the underlying Bianchi spacetime are oscillatory. To summarise, there seems to be a universality as far as the asymptotics in the direction of silent singularities are concerned. In fact, it is tempting to conjecture that as long as the singularity of the underlying Bianchi spacetime is silent, then the asymptotics of solutions are as described above. In order to contrast the above asymptotics with the non-silent setting, we, by appealing to known results, provide a complete asymptotic characterisation of solutions to the Klein-Gordon equation on a flat Kasner background. In that setting, us does, generically, not converge.</p>
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5.
  • Ringström, Hans, 1972- (författare)
  • On the future stability of cosmological solutions to Einstein's equations with accelerated expansion
  • 2014
  • Ingår i: PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL II. - KyungMoonSa Publishers. - 978-89-6105-805-6 ; s. 983-999
  • Konferensbidrag (refereegranskat)abstract
    • <p>The solutions of Einstein's equations used by physicists to model the universe have a high degree of symmetry. In order to verify that they are reasonable models, it is therefore necessary to demonstrate that they are future stable under small perturbations of the corresponding initial data. The purpose of this contribution is to describe mathematical results that have been obtained on this topic. A question which turns out to be related concerns the topology of the universe: what limitations do the observations impose? Using methods similar to ones arising in the proof of future stability, it is possible to construct solutions with arbitrary closed spatial topology. The existence of these solutions indicate that the observations might not impose any limitations at all.</p>
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6.
  • Ringström, Hans, 1972- (författare)
  • On the Topology and Future Stability of the Universe
  • 2013. - 1
  • Bok (refereegranskat)abstract
    • <p>The subject of the book is the topology and future stability of models of the universe. In standard cosmology, the universe is assumed to be spatially homogeneous and isotropic. However, it is of interest to know whether perturbations of the corresponding initial data lead to similar solutions or not. This is the question of stability. It is also of interest to know what the limitations on the global topology imposed by observational constraints are. These are the topics addressed in the book. The theory underlying the discussion is the general theory of relativity. Moreover, in the book, matter is modelled using kinetic theory. As background material, the general theory of the Cauchy problem for the Einstein–Vlasov equations is therefore developed.</p>
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