| 1. |
- 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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| 2. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system.
- 2010
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Ingår i: Quarterly of Applied Mathematics. - 1552-4485. ; 68, s. 17-42
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Tidskriftsartikel (refereegranskat)abstract
- We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution. Among these data there are data such that the corresponding solutions exist globally in Schwarzschild coordinates. We put these results into a more general context, and we include arguments which show that the spacetimes we obtain satisfy the weak cosmic censorship conjecture and contain a black hole in the sense of suitable mathematical definitions of these concepts which are available in the literature.
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| 3. |
- Andreasson, Håkan, 1966
(författare)
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Regularity Results for the Spherically Symmetric Einstein-Vlasov System
- 2010
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 11:5, s. 781-803
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Tidskriftsartikel (refereegranskat)abstract
- The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose of the present work is to propose a method of approach for general initial data, which improves the regularity of the terms that need to be estimated compared to previous methods. We prove that global existence holds outside the center in both these coordinate systems. In the Schwarzschild case we improve the bound on the momentum support obtained in Rein et al. (Commun Math Phys 168:467-478, 1995) for compact initial data. The improvement implies that we can admit non-compact data with both ingoing and outgoing matter. This extends one of the results in Andreasson and Rein (Math Proc Camb Phil Soc 149:173-188, 2010). In particular our method avoids the difficult task of treating the pointwise matter terms. Furthermore, we show that singularities never form in Schwarzschild time for ingoing matter as long as 3m <= r. This removes an additional assumption made in Andreasson (Indiana Univ Math J 56:523-552, 2007). Our result in maximal-isotropic coordinates is analogous to the result in Rendall (Banach Center Publ 41:35-68, 1997), but our method is different and it improves the regularity of the terms that need to be estimated for proving global existence in general.
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| 4. |
- Andreasson, Håkan, 1966, et al.
(författare)
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The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse
- 2010
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Ingår i: Mathematical proceedings of the Cambridge Philosophical Society. - 0305-0041 .- 1469-8064. ; 149:1, s. 173-188
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Tidskriftsartikel (refereegranskat)abstract
- Given a static Schwarzschild spacetime of ADM mass M, it is well known that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time. We show that in gravitational collapse of Vlasov matter this behaviour can be very different. We construct initial data for which a black hole forms and all matter crosses the event horizon as Schwarzschild time goes to infinity, and show that this is a necessary condition for geodesic completeness of the event horizon. In addition to a careful analysis of the asymptotic behaviour of the matter characteristics our proof requires a new argument for global existence of solutions to the spherically symmetric Einstein–Vlasov system in an outer domain, since our initial data have non-compact support in the radial momentum variable and previous methods break down.
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| 5. |
- Morén, Håkan, et al.
(författare)
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Multifocal electroretinogram for functional evaluation of retinal injury following ischemia-reperfusion in pigs.
- 2010
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Ingår i: Graefe's Archive for Clinical and Experimental Ophthalmology. - : Springer Science and Business Media LLC. - 1435-702X .- 0721-832X. ; 248, s. 627-634
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: Multifocal electroretinogram (mfERG) has the power to discriminate between localized functional losses and overall retinal changes when evaluating retinal injury. So far, full-field ERG has been the gold standard for examining retinal ischemia and the effects of different neuroprotectants in experimental conditions. The aim of the present study was to establish mfERG, with simultaneous fundus monitoring, for analyzing the localized functional response in the retina after ischemia-reperfusion in the porcine eye. METHODS: 70 kg pigs underwent pressure-induced retinal ischemia (1 hour) followed by reperfusion. mfERG recordings were obtained before and after ischemia, followed by 1 and 5 hours of reperfusion. Individual components of the summed mfERG responses were correlated to ischemia and the time of reperfusion. RESULTS: The visual streak area had significantly higher amplitudes than the optic nerve head and the area in between, suggesting that the mfERG monitors localized functional retinal responses. The mfERG recordings were altered following ischemia-reperfusion. In one group of animals, there was a complete flattening of the mfERG waveforms, indicating complete ischemic injury. In the other group of animals, ischemia-reperfusion altered the mfERG such that the implicit time was increased (20.82 +/- 0.18 before ischemia and 21.57 +/- 0.21 after ischemia and 1 hour of reperfusion, in the visual streak area, p < 0.05) and the amplitude was decreased (13.16 +/- 2.3 before ischemia and 11.47 +/- 0.88 after ischemia and 1 hour of reperfusion, in the visual streak area, p < 0.001), suggesting partial ischemic injury. CONCLUSIONS: In conclusion, the porcine model of pressure-induced retinal ischemia-reperfusion results in mfERG changes, typical for retinal ischemia. mfERG may be a useful tool for evaluating and monitoring localized cone dysfunction after an ischemic injury.
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