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- Andreasson, Håkan, 1966, et al.
(författare)
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A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein–Vlasov system
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23, s. 3659-3677
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Tidskriftsartikel (refereegranskat)abstract
- The stability features of steady states of the spherically symmetric Einstein–Vlasov system are investigated numerically. We find support for the conjecture by Zel'dovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.
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| 3. |
- 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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| 4. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Bounds on M/R for static objects with a positive cosmological constant
- 2009
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:19, s. 195007-
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Tidskriftsartikel (refereegranskat)abstract
- We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant Λ, which are regular at the centre, and we investigate the influence of Λ on the bound of M/R, where M is the ADM mass and R is the area radius of the boundary of the static object. We find that for any solution which satisfies the energy condition p + 2p ⊥ ≤ ρ, where p ≥ 0 and p ⊥ are the radial and tangential pressures respectively, and ρ ≥ 0 is the energy density, and for which 0 ≤ ΛR 2 ≤ 1, the inequality holds. If Λ = 0, it is known that infinitely thin shell solutions uniquely saturate the inequality, i.e. the inequality is sharp in that case. The situation is quite different if Λ > 0. Indeed, we show that infinitely thin shell solutions do not generally saturate the inequality except in the two degenerate situations ΛR 2 = 0 and ΛR 2 = 1. In the latter situation there is also a constant density solution, where the exterior spacetime is the Nariai solution, which saturates the inequality; hence, the saturating solution is non-unique. In this case the cosmological horizon and the black hole horizon coincide. This is analogous to the charged situation where there is numerical evidence that uniqueness of the saturating solution is lost when the inner and outer horizons of the Reissner-Nordström solution coincide. © 2009 IOP Publishing Ltd.
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| 6. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
- 2008
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Ingår i: Communications in Partial Differential Equations. - : Informa UK Limited. - 0360-5302 .- 1532-4133. ; 33:4, s. 656-668
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Tidskriftsartikel (refereegranskat)abstract
- We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.
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| 9. |
- Andreasson, Håkan, 1966
(författare)
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On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates
- 2007
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Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 56, s. 523-552
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Tidskriftsartikel (refereegranskat)abstract
- The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e., polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other types of criteria which prevent finite time blow-up are also given.
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| 10. |
- 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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