| 11. |
- 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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| 12. |
- Andreasson, Håkan, 1966
(författare)
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On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system
- 2014
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Ingår i: AIP Conference Proceedings: Plasma Physics and Relativistic Fluids. - : AIP Publishing LLC. - 0094-243X .- 1551-7616. - 9780735412088 ; 1578, s. 129-139
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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<4/9, where M is the ADM mass and R the outer radius. Most static solutions of the Einstein-Vlasov system do not satisfy these assumptions. The bound M/R<4/9 nevertheless holds and it is sharp. An analogous bound in the charged case is also given. The important question of stability of spherically symmetric static solutions is presently open but numerical results are available and these are reviewed. A natural question is to go beyond spherical symmetry and consider axially symmetric solutions, and a recent result on the existence of axially symmetric stationary solutions is also discussed.
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| 13. |
- Andréasson, Håkan, et al.
(författare)
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Outcome differences between debulking surgery and cytoreductive surgery in patients with pseudomyxoma peritonei
- 2012
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Ingår i: European Journal of Surgical Oncology. - : Elsevier BV. - 0748-7983 .- 1532-2157. ; 38:10, s. 962-968
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND:The aim of this study was to compare debulking surgery and cytoreductive surgery (CRS) in patients with Pseudomyxoma peritonei (PMP) regarding efficacy and safety.PATIENTS AND METHODS:Data were extracted from medical records and treatment outcomes were analyzed for all 152 patients with PMP who were scheduled for debulking surgery and intraperitoneal chemotherapy (IPC) or CRS and IPC at Uppsala University Hospital, Uppsala, Sweden, between September 1993 and December 2008.RESULTS:One hundred and ten patients (73%) were treated with CRS and IPC and 40 (27%) with debulking surgery and IPC. In two patients (1%), surgery was defined as open and close. Patients with CRS and IPC had a 74% 5-year overall survival (OS) rate compared with 40% for those treated with debulking surgery (P < 0.001). Patients with no residual macroscopic tumour (R1 resection) had a better 5-year OS rate of 94% compared with 28% for patients with macroscopic residual tumour (R2) (P < 0.001). Grades II-IV adverse events were seen in 29% of debulked patients and in 47% of CRS/IPC patients (P = 0.053).CONCLUSIONS:CRS and IPC seems more efficient than debulking surgery and IPC but with numerically higher morbidity. Therefore, if surgically possible, CRS should be the treatment of choice for PMP patients. However, debulking surgery may still be of benefit to selected patients for palliative purposes.
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| 14. |
- Andréasson, Håkan
(författare)
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Pseudomyxoma Peritonei : Aspects of Natural History, Learning Curve, Treatment Outcome and Prognostic Factors
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Pseudomyxoma peritonei (PMP) is a rare disease characterized by mucinous peritoneal metastasis (PM). Different loco-regional treatment strategies, i.e. debulking surgery and cytoreductive surgery (CRS) in combination with hyperthermic intraperitoneal chemotherapy (HIPEC), have changed the prognosis for these patients. CRS is an aggressive surgical procedure with a long learning curve. PMP exists in different types; how many depends on which classification is used.The aims of this thesis were to investigate the time-frame of PMP development from an isolated appendiceal neoplasm, examine the learning process for CRS, evaluate the differences in treatment outcome between debulking surgery and CRS in combination with HIPEC, to evaluate a more detailed PMP classification and to investigate particularly interesting new cysteine-histidine (PINCH) protein as a prognostic factor for PMP.Retrospectively 26 PMP patients were identified as having had an appendectomy with a neoplasm in the appendix but with no evidence of PM at the appendectomy. They were treated for PMP within a median of 13.1 months (3.8-95.3) after the appendectomy. No difference was seen between the types of PMP regarding the time to a clinically significant development of PMP and how much tumour was found at treatment. CRS is a highly invasive treatment and stabilization in the learning curve was seen after 220±10 procedures. Patients treated with CRS+HIPEC had a better 5-year overall survival (OS) than patients treated with debulking surgery, 74% vs. 40%. CRS increased the rate of complete cytoreduction from 25% in patients treated with debulking surgery to 72%. The new four-grade PMP classification showed very good inter-rater agreement between two independent pathologists and a difference in survival rates was observed between the different grades. A positive PINCH staining was recorded in 83% of the tumours and that was associated with poorer survival.
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| 15. |
- 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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| 16. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter
- 2014
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 329:2, s. 787-808
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Tidskriftsartikel (refereegranskat)abstract
- The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This pro- vides mathematical models for rotating, general relativistic and asymptotically flat non- vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on R 5.
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| 17. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Spherically symmetric steady states of John elastic bodies in general relativity
- 2014
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:16
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Tidskriftsartikel (refereegranskat)abstract
- We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large (z approximate to 2.8) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.
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| 18. |
- Andreasson, Håkan, 1966, et al.
(författare)
-
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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| 19. |
- Andreasson, Håkan, 1966
(författare)
-
The Einstein-Vlasov system/Kinetic theory
- 2011
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Ingår i: Living Reviews in Relativity. - : Springer Science and Business Media LLC. - 1433-8351 .- 2367-3613. ; 14
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Tidskriftsartikel (refereegranskat)abstract
- The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
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| 20. |
- Andreasson, Håkan, 1966, et al.
(författare)
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The formation of black holes in spherically symmetric gravitational collapse
- 2011
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Ingår i: MATHEMATISCHE ANNALEN. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 350:3, s. 683-705
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Tidskriftsartikel (refereegranskat)abstract
- We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines r=c [0,2M] are incomplete, and for r > 2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We give examples of such initial data with the additional property that the solutions exist for all r ≥ 0 and all Schwarzschild time, i. e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.
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