| 1. |
- Ames, Ellery, et al.
(författare)
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A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges
- 2017
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Ingår i: Journal of Geometry and Physics. - : Elsevier. - 0393-0440 .- 1879-1662. ; 121, s. 42-71
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Tidskriftsartikel (refereegranskat)abstract
- We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which has so far been known to hold for solutions in areal coordinates only, is stable to perturbations of the coordinate systems. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.
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| 2. |
- 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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| 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, et al.
(författare)
-
Hoop and weak cosmic censorship conjectures for the axisymmetric Einstein-Vlasov system
- 2023
-
Ingår i: Physical Review D. - 2470-0010 .- 2470-0029. ; 108:6
-
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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| 5. |
- 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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| 6. |
- Ames, Ellery, 1984, et al.
(författare)
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Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems
- 2024
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Ingår i: Classical and Quantum Gravity. - 0264-9381 .- 1361-6382. ; 41:7
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Forskningsöversikt (refereegranskat)abstract
- The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav. 33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw. 8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.
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