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Sökning: WFRF:(Andreasson Håkan)

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  • Andreasson, Håkan, 1966- (författare)
  • On gravitational collapse and cosmic censorship for collisionless matter
  • 2014
  • Ingår i: International Journal of Geometric Methods in Modern Physics. - 0219-8878. ; 11:2
  • Tidskriftsartikel (refereegranskat)abstract
    • The weak cosmic censorship conjecture is a central open problem in classical general relativity. Under the assumption of spherical symmetry, Christodoulou has investigated the conjecture for two different matter models; a scalar field and dust. He has shown that the conjecture holds true for a scalar field but that it is violated in the case of dust. The outcome of the conjecture is thus sensitive to which model is chosen to describe matter. Neither a scalar field nor dust are realistic matter models. Collisionless matter, or Vlasov matter, is a simple matter model but can be considered to be realistic in the sense that it is used by astrophysicists. The present status on the weak cosmic censorship conjecture for the Einstein-Vlasov system is reviewed here.
  • Andreasson, Håkan, 1966- (författare)
  • On Lorentz Invariance, Regularity and Global Existence for Kinetic Equations
  • 1997
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • [A1] Regularity of the gain term and strong L1 convergence to equilibrium for the relativistic Boltzmann equation. The main purpose of the paper is to show that the gain term of the relativistic collision operator is regularizing. This is a generalization of P.L. Lions' analogous result in the nonrelativistic situation. The Lorentz invariance of relativistic particle dynamics plays an important role in the proof. The regularizing theorem has many applications in kinetic theory, some of which are discussed in the paper. In particular the asymptotic behaviour of periodic solutions to the relativistic Boltzmann equation is studied. It is shown that such solutions converge strongly in L^1 to a global Juttner equilibrium solution for arbitrary initial data. This extends earlier results for small data.<p /> [A2] Global existence of smooth solutions in three dimensions for the semiconductor Vlasov-Poisson-Boltzman equation. This paper shows global existence and uniqueness of smooth solutions in three dimensions for the semiconductor Vlasov-Poisson-Boltzmann equation. This extends an earlier result from the two-dimensional situation. Moreover, assumptions on the scattering kernel which limit the decay of the collision frequency are introduced, extending in part the assumptions used in the two-dimensional case. A slow decay of the collision frequency is important for studying fluid approximations under high electric fields of the Vlasov-Poisson-Boltzmann equation.<p /> [A3] Controlling the propagation of the support for the relativistic Vlasov equation with a selfconsistent Lorentz invariant field. The motivation for this paper comes from the fact that the successful techniques developed for controlling the propagation of the support for the classical Vlasov-Poisson equation (leading to global existence of smooth solutions) all fail for the relativistic Vlasov-Poisson equation. This equation lacks the Lorentz invariance. It has nevertheless been suggested that an understanding of this equation may be necessary for understanding the fundamental relativistic Vlasov-Maxwell equation. In the paper a new equation for the field is introduced which is Lorentz invariant. It is shown that the propagation of the support, for solutions satisfying this equation and the relativistic Vlasov equation, may be controlled. This is a strong indication that the transformation properties of the equations are important in studying existence of smooth solutions.
  • Andreasson, Håkan, 1966- (författare)
  • On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System
  • 2007
  • Ingår i: Communications in Mathematical Physics. - 1432-0916 .- 0010-3616. ; 274:2, s. 409-425
  • Tidskriftsartikel (refereegranskat)abstract
    • In a previous work [1] matter models such that the energy density ρ 0, and the radial- and tangential pressures p 0 and q, satisfy p + q Ωρ, Ω 1, were considered in the context of Buchdahl's inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R 0, R 1], R 0 &gt; 0, satisfies R 1/R 0 &lt; 1/4. Moreover, given a sequence of solutions such that R 1/R 0 → 1, then the limit supremum of 2M/R 1 was shown to be bounded by ((2Ω + 1)2 - 1)/(2Ω + 1)2. In this paper we show that the hypothesis that R 1/R 0 → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R 1 is bounded, but that the limit is ((2Ω + 1)2 - 1)/(2Ω + 1)2 = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R 1 arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R 1 of any static solution of the spherically symmetric Einstein-Vlasov system.
  • Andreasson, Håkan, 1966- (författare)
  • On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system
  • 2014
  • Ingår i: AIP Conference Proceedings: Plasma Physics and Relativistic Fluids. - 0094-243X. - 978-0-7354-1208-8 ; 1578, s. 129-139
  • Konferensbidrag (refereegranskat)abstract
    • The present status on the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system is reviewed. Under the assumptions that a spherically symmetric static object has isotropic pressure and non-increasing energy density outwards, Buchdahl showed 1959 the bound M/R
  • Andreasson, Håkan, 1966-, et al. (författare)
  • On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
  • 2015
  • Ingår i: Monthly notices of the Royal Astronomical Society. - 0035-8711. ; 446:4, s. 3932-3942
  • Tidskriftsartikel (refereegranskat)abstract
    • A large class of flat axially symmetric solutions to the Vlasov–Poisson system is constructed with the property that the corresponding rotation curves are approximately flat, slightly decreasing or slightly increasing. The rotation curves are compared with measurements from real galaxies and satisfactory agreement is obtained. These facts raise the question whether the observed rotation curves for disc galaxies may be explained without introducing dark matter. Furthermore, it is shown that for the ansatz we consider stars on circular orbits do not exist in the neighbourhood of the boundary of the steady state.
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