2001年11月7日
Stability criterion for self-similar solutions with perfect fluids in general relativity
Classical and Quantum Gravity
- 巻
- 18
- 号
- 21
- 開始ページ
- 4549
- 終了ページ
- 4567
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1088/0264-9381/18/21/311
- 出版者・発行元
- IOP PUBLISHING LTD
A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state P = kp in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink mode. The criterion is directly related to the classification of sonic points. The criterion gives a sufficient condition for instability of the solution. For a transonic point in collapse, all primary-direction nodal-point solutions are unstable, while all secondary-direction nodal-point solutions and saddle-point ones are stable against the kink mode. The situation is reversed in expansion. The applications are the following: the expanding flat Friedmann solution for 1/3 ≤ k <
1 and the collapsing one for 0 <
k ≤ 1/3 are unstable
the static self-similar solution is unstable
nonanalytic self-similar collapse solutions are unstable
the Larson-Penston (attractor) solution is stable for this mode for 0 <
k ≲ 0.036, while it is unstable for 0.036 ≲ k
the Evans-Coleman (critical) solution is stable for this mode for 0 <
k ≲ 0.89, while it is unstable for 0.89 ≲ k. The last application suggests that the Evans-Coleman solution for 0.89 ≲ k is not critical because it has at least two unstable modes.
1 and the collapsing one for 0 <
k ≤ 1/3 are unstable
the static self-similar solution is unstable
nonanalytic self-similar collapse solutions are unstable
the Larson-Penston (attractor) solution is stable for this mode for 0 <
k ≲ 0.036, while it is unstable for 0.036 ≲ k
the Evans-Coleman (critical) solution is stable for this mode for 0 <
k ≲ 0.89, while it is unstable for 0.89 ≲ k. The last application suggests that the Evans-Coleman solution for 0.89 ≲ k is not critical because it has at least two unstable modes.
- リンク情報
- ID情報
-
- DOI : 10.1088/0264-9381/18/21/311
- ISSN : 0264-9381
- eISSN : 1361-6382
- SCOPUS ID : 0035540101
- Web of Science ID : WOS:000172474000012