| 1. |
- Ames, Ellery, et al.
(författare)
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Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity
- 2019
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Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 99:2
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Tidskriftsartikel (refereegranskat)abstract
- We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have nonvanishing angular momentum. As the parameters are tuned to more relativistic solutions (measured e.g., by an increasing redshift) we provide evidence for a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become locally rotationally symmetric about the matter density. The existence of a deficit angle in these regions is investigated.
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| 2. |
- Ames, E., et al.
(författare)
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Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system
- 2021
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 38:10
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Tidskriftsartikel (refereegranskat)abstract
- We numerically investigate the dynamics near black hole formation of solutions to the Einstein-Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the (2 + 1) + 1 formulation of the Einstein field equations in axisymmetry. Solutions are launched from non-stationary initial data and exhibit type I critical behaviour. In particular, we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy.
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| 3. |
- Ames, Ellery, et al.
(författare)
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Hoop and weak cosmic censorship conjectures for the axisymmetric Einstein-Vlasov system
- 2023
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Ingår i: Physical Review D. - 2470-0010 .- 2470-0029. ; 108:6
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Tidskriftsartikel (refereegranskat)abstract
- We consider gravitational collapse for the axially symmetric Einstein-Vlasov system. We investigate the weak cosmic censorship conjecture in the case of highly prolate initial data and we investigate the "only if"part of the Hoop conjecture. Shapiro and Teukolsky initiated a similar study in 1991 [Formation of Naked Singularities: The Violation of Cosmic Censorship, Phys. Rev. Lett. 66, 994 (1991)PRLTAO0031-900710.1103/PhysRevLett.66.994] where they found support that the weak cosmic censorship conjecture was violated for sufficiently prolate spheroidal initial data. More recently, independent studies of this problem have been carried out by Yoo et al. [3D simulation of spindle gravitational collapse of a collisionless particle system, Classical Quantum Gravity 34, 105010 (2017)CQGRDG0264-938110.1088/1361-6382/aa6ad5] and by East [Cosmic Censorship Upheld in Spheroidal Collapse of Collisionless Matter, Phys. Rev. Lett. 122, 231103 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.231103]. A common feature in these works is that the initial data are dustlike. Dust can be considered as a singular case of matter described by the Einstein-Vlasov system. The original motivation by Shapiro and Teukolsky to study this problem is based on the Lin-Mestel-Shu instability for gravitational collapse of uniform spheroids in the case of dust in Newtonian gravity. We argue that the Lin-Mestel-Shu solution is not relevant for studying the weak cosmic censorship conjecture of the Einstein-Vlasov system and we argue that dustlike initial data is also not relevant. To investigate collapse of highly prolate spheroidal configurations for the Einstein-Vlasov system is nevertheless interesting in view of the Hoop conjecture. By choosing highly prolate initial data the weak cosmic censorship conjecture is seriously tested. We carry out such a study for initial data which are not dustlike. We find formation of an apparent horizon in all cases we consider, which provides support for the weak cosmic censorship conjecture. In our tests of the Hoop conjecture we compute the polar circumference CH,p at the time when the apparent horizon forms and find that it is less than 12% above 4πM, where M is the irreducible mass of the apparent horizon, which agrees with the spirit of the Hoop conjecture.
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| 4. |
- Ames, Ellery, 1984, et al.
(författare)
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On axisymmetric and stationary solutions of the self-gravitating Vlasov system
- 2016
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 33:15
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Tidskriftsartikel (refereegranskat)abstract
- Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
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| 5. |
- 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 EinsteinVlasov 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 EinsteinVlasov 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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