| 1. |
- Andreasson, Håkan, 1966
(författare)
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On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System
- 2007
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 274, s. 409-425
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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 > 0, satisfies R 1/R 0 < 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.
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| 2. |
- Ames, Ellery, et al.
(författare)
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Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity
- 2019
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Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 99:2
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Tidskriftsartikel (refereegranskat)abstract
- We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have nonvanishing angular momentum. As the parameters are tuned to more relativistic solutions (measured e.g., by an increasing redshift) we provide evidence for a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become locally rotationally symmetric about the matter density. The existence of a deficit angle in these regions is investigated.
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| 3. |
- Ames, E., et al.
(författare)
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Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system
- 2021
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:10
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Tidskriftsartikel (refereegranskat)abstract
- We numerically investigate the dynamics near black hole formation of solutions to the Einstein-Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the (2 + 1) + 1 formulation of the Einstein field equations in axisymmetry. Solutions are launched from non-stationary initial data and exhibit type I critical behaviour. In particular, we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy.
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| 4. |
- Andreasson, Håkan, 1966, et al.
(författare)
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A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system
- 2009
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:14
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Tidskriftsartikel (refereegranskat)abstract
- We construct, by numerical means, static solutions of the spherically symmetric Einstein-Vlasov-Maxwell system and investigate various features of the solutions. This extends a previous investigation (Andreasson and Rein 2007 Class. Quantum Grav. 24 1809) of the chargeless case. We study the possible shapes of the energy density profile as a function of the area radius when the electric charge of an individual particle is varied as a parameter. We find profiles which are multi-peaked, where the peaks are separated either by vacuum or a thin atmosphere, and we find that for a sufficiently large charge parameter the solutions break down at a finite radius. Furthermore, we investigate the inequality root M <= root R/3 + root R/9 + Q(2)/3R, which is derived in Andreasson (2009 Commun. Math. Phys. 288 715) for general matter models, and we find that it is sharp for the Einstein-Vlasov-Maxwell system. Here M is the ADM mass, Q is the charge and R is the area radius of the boundary of the static object. We find two classes of solutions with this property, while there is only one in the chargeless case. In particular we find numerical evidence for the existence of arbitrarily thin shell solutions to the Einstein-Vlasov-Maxwell system. Finally, we consider one-parameter families of steady states, and we find spirals in the mass-radius diagram for all examples of the microscopic equation of state which we consider.
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| 5. |
- Andreasson, Håkan, 1966
(författare)
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Existence of Steady States of the Massless Einstein-Vlasov System Surrounding a Schwarzschild Black Hole
- 2021
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 22
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Tidskriftsartikel (refereegranskat)abstract
- We show that there exist steady states of the spherically symmetric massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole. We also include a numerical investigation about the properties of the shells.
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| 6. |
- Andreasson, Håkan, 1966, et al.
(författare)
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On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
- 2015
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Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press (OUP). - 0035-8711 .- 1365-2966. ; 446:4, s. 3932-3942
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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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| 7. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Comments on the paper ‘Static solutions of the Vlasov–Einstein system’ by G. Wolansky
- 2020
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Ingår i: Archive for Rational Mechanics and Analysis. - : Springer Science and Business Media LLC. - 1432-0673 .- 0003-9527. ; 235:1, s. 783-791
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Tidskriftsartikel (refereegranskat)abstract
- In this note we address the attempted proof of the existence of static solutions to the Einstein–Vlasov system as given in Wolansky (Arch Ration Mech Anal 156:205–230, 2001). We focus on a specific and central part of the proof which concerns a variational problem with an obstacle. We show that two important claims in Wolansky (2001) are incorrect and we question the validity of a third claim. We also discuss the variational problem and its difficulties with the aim of stimulating further investigation of this intriguing problem in particular answering the question of whether or not static solutions of the Einstein–Vlasov system can be found as local minimizers of an energy-Casimir functional.
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| 8. |
- Andreasson, Håkan, 1966
(författare)
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On gravitational collapse and cosmic censorship for collisionless matter
- 2014
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Ingår i: International Journal of Geometric Methods in Modern Physics. - : World Scientific Pub Co Pte Lt. - 0219-8878 .- 1793-6977. ; 11:2
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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.
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| 9. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Existence of axially symmetric static solutions of the Einstein-Vlasov system
- 2011
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Ingår i: Commun. Math. Phys.. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 308, s. 23-47
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Tidskriftsartikel (refereegranskat)abstract
- We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.
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| 10. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
- 2010
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Ingår i: Journal of Hyperbolic Differential Equations. - Göteborg : Chalmers University of Technology. - 0219-8916. ; 7:4, s. 707-731
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Tidskriftsartikel (refereegranskat)abstract
- We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.
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