| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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