A numerical stability analysis for the Einstein-Vlasov system

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-paramete...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 38; no. 3; pp. 35003 - 35029
Main Authors Günther, Sebastian, Körner, Jacob, Lebeda, Timo, Pötzl, Bastian, Rein, Gerhard, Straub, Christopher, Weber, Jörg
Format Journal Article
LanguageEnglish
Published IOP Publishing 05.02.2021
Subjects
binding energy
black hole
collapse
Einstein-Vlasov
heteroclinic orbit
Matematik
Matematisk analys
Mathematical Analysis
Mathematics
Natural Sciences
Naturvetenskap
stability
turning point
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Summary: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.
Bibliography:CQG-107522.R1
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/abcbdf