| 11. |
- 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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| 12. |
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| 13. |
- Andreasson, Håkan, 1966
(författare)
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Black hole formation from a complete past for the einstein–vlasov system
- 2014
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Ingår i: International conference on Relativity and Gravitation, 2012, Prague, Czech Republic, 25-29 June 2012. - Cham : Springer International Publishing. - 0930-8989 .- 1867-4941. - 9783319067605 ; 157, s. 11-18
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Konferensbidrag (refereegranskat)abstract
- Anatural question in general relativity is to find initial data for the Einstein equations whose past evolution is regular and whose future evolution contains a black hole. In [1] initial data of this kind is constructed for the spherically symmetric Einstein–Vlasov system. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass (Formula presented) (r) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is analogous to the result [2] for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time t ∈ (−∞,∞). In the present article we review the results in [1].
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| 14. |
- Andreasson, Håkan, 1966
(författare)
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Black Hole Formation from a Complete Regular Past for Collisionless Matter
- 2012
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Ingår i: Annales Henri Poincaré. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 13:7, s. 1511-1536
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Tidskriftsartikel (refereegranskat)abstract
- Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a "realistic" matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass mIS= mIS (r) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is in a sense analogous to the result (Christodoulou Commun Pure Appl Math 44:339-373, 1991) for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time .
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| 15. |
- Andreasson, Håkan, 1966
(författare)
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Black hole formation from a complete regular past for vlasov matter
- 2013
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Ingår i: XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012. - : WORLD SCIENTIFIC. ; , s. 365-372
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- A natural question in general relativity is to find initial data for the Einstein equations whose past evolution is regular and whose future evolution contains a black hole. In [1] initial data of this kind is constructed for the spherically symmetric Einstein-Vlasov system. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass (forumal presented) and the area radius r is arbitrarily small everywhere, such that a black hole forms in the evolution. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time t ? (-?, ?). In the present article we review the results in [1]. © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
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| 16. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Bounds on M/R for charged objects with positive cosmological constant
- 2012
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 29:9
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Tidskriftsartikel (refereegranskat)abstract
- We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant Lambda. If r denotes the area radius, m(g) and q the gravitational mass and charge of a sphere with area radius r respectively, we find that for any solution which satisfies the condition p + 2p(perpendicular to) +/- <= rho, where p >= 0 and p(perpendicular to) are the radial and tangential pressures respectively, rho >= 0 is the energy density, and for which 0 <= q(2)/r(2) + Lambda r(2) <= 1, the inequality m(g)/r <= 2/9 + q(2)/3r(2)-Lambda r(2)/3 + 2/9 root 1 + 3q(2)/r(2) + 3 Lambda r(2) holds. We also investigate the issue of sharpness, and we showthat the inequality is sharp in a few cases but generally this question is open.
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| 17. |
- 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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| 18. |
- 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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| 19. |
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| 20. |
- Andréasson, Håkan, et al.
(författare)
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Cytoreductive surgery in pseudomyxoma peritonei-aspects of the learning curve
- 2013
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Ingår i: European Journal of Surgical Oncology. - : Elsevier BV. - 0748-7983 .- 1532-2157. ; 40:8, s. 930-936
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Tidskriftsartikel (refereegranskat)abstract
- Background: Cytoreductive surgery (CRS) plus perioperative intraperitoneal chemotherapy is a highly invasive treatment of peritoneal metastasis and requires many surgical procedures before mastering. The aim of this study was to estimate how many procedures are needed before stabilization can be seen in surgical outcome (R1 surgery, adverse events and bleeding) in patients with pseudomyxoma peritonei (PMP). Patients and methods: All 128 patients with PMP who were treated with CRS alone or CRS plus perioperative intraperitoneal chemotherapy between 2003 and 2008 at the Uppsala University Hospital, Uppsala, Sweden, were included. The learning curve was calculated using the partial least square (PLS) and cumulative sum control chart (CUSUM) graph. Two groups were formed based on the results of the learning curve. The learning curve plateau was considered the same as the stabilization in the CUSUM graph. Group I consisted of patients included during the learning period (n = 73) and Group 11 of patients treated after the learning period ended (n = 55). Comparisons between the groups were made on surgical outcome, survival and adverse events. Results: Stabilization was seen after 220 +/- 10 procedures. A higher occurrence of R1 surgery was seen in Group H (80%) compared to Group I (48%; P = 0.0002). Overall survival increased at four years after surgery in Group H compared to Group I (80% vs. 63%; P = 0.02). Conclusion: CRS plus perioperative intraperitoneal chemotherapy is a highly demanding procedure that requires more than 200 procedures before optimisation in surgical outcome is seen.
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