A numerical stability analysis for the Einstein-Vlasov system
(2021) In Classical and Quantum Gravity 38(3).- Abstract
We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical... (More)
We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical reliability of the latter is strengthened by obtaining consistent results in the three different coordinate systems and by the systematic use of dynamically accessible perturbations.
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- author
- Günther, Sebastian ; Körner, Jacob ; Lebeda, Timo ; Pötzl, Bastian ; Rein, Gerhard ; Straub, Christopher and Weber, Jörg LU
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- binding energy, black hole, collapse, Einstein-Vlasov, heteroclinic orbit, stability, turning point
- in
- Classical and Quantum Gravity
- volume
- 38
- issue
- 3
- article number
- 035003
- publisher
- IOP Publishing
- external identifiers
-
- scopus:85099042417
- ISSN
- 0264-9381
- DOI
- 10.1088/1361-6382/abcbdf
- language
- English
- LU publication?
- yes
- id
- 1c9bfc0d-9fd3-46fb-86f3-f707dee0df89
- date added to LUP
- 2021-01-19 10:20:14
- date last changed
- 2022-04-26 23:45:34
@article{1c9bfc0d-9fd3-46fb-86f3-f707dee0df89,
abstract = {{<p>We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical reliability of the latter is strengthened by obtaining consistent results in the three different coordinate systems and by the systematic use of dynamically accessible perturbations. </p>}},
author = {{Günther, Sebastian and Körner, Jacob and Lebeda, Timo and Pötzl, Bastian and Rein, Gerhard and Straub, Christopher and Weber, Jörg}},
issn = {{0264-9381}},
keywords = {{binding energy; black hole; collapse; Einstein-Vlasov; heteroclinic orbit; stability; turning point}},
language = {{eng}},
number = {{3}},
publisher = {{IOP Publishing}},
series = {{Classical and Quantum Gravity}},
title = {{A numerical stability analysis for the Einstein-Vlasov system}},
url = {{http://dx.doi.org/10.1088/1361-6382/abcbdf}},
doi = {{10.1088/1361-6382/abcbdf}},
volume = {{38}},
year = {{2021}},
}