Geodetický chaos v porušených polích černých děr
| Název práce v češtině: | Geodetický chaos v porušených polích černých děr |
|---|---|
| Název v anglickém jazyce: | Geodesic chaos in perturbed black-hole fields |
| Klíčová slova: | obecná relativita a gravitace, geodetický pohyb, černé díry, chaotická dynamika |
| Klíčová slova anglicky: | general relativity and gravitation, geodesic motion, black holes, chaotic dynamics |
| Akademický rok vypsání: | 2020/2021 |
| Typ práce: | disertační práce |
| Jazyk práce: | čeština |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | doc. Mgr. Tomáš Ledvinka, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 08.09.2020 |
| Datum zadání: | 08.09.2020 |
| Datum potvrzení stud. oddělením: | 06.10.2020 |
| Konzultanti: | Mgr. Petra Suková, Ph.D. |
| Zásady pro vypracování |
| Dynamics of time-like geodesics will be studied numerically in the field of a Schwarzschild black hole perturbed, in the first order, by a rotating light finite thin disc [2]. Poincaré diagrams will be plotted first, with other methods applied possibly in specific cases (see references to previous papers in [1] etc.). The task includes the following steps: i) Modify the existing code (applicable to static and axisymmetric vacuum metrics) in order to include the linear rotational perturbation as described in [2]. ii) Run the respective numerical simulations. iii) Assess the effect of disc crossings in either static or rotating settings. iv) Possibly consider/suggest new methods how to detect, evaluate and classify geodesic chaos. v) Additional option: compare, analytically, the perturbative metric [2] with other exact or approximate solutions of similar interpretation. |
| Seznam odborné literatury |
| [1] Polcar L., Semerák O., Phys. Rev. D 100 (2019) 103013
[2] Semerák O., Čížek P., Universe 6 (2020) 27 Textbooks on general relativity and black holes (e.g. Frolov V. P., Novikov I. D., Black Hole Physics, Fundamental Theories of Physics vol. 96, Springer, Dordrecht 1998) and on chaotic dynamics (e.g. Elhadj Z., Dynamical Systems: Theories and Applications, CRC Press 2019). |
| Předběžná náplň práce |
| Geodesic motion is completely integrable in the fields of isolated stationary black holes, but it may become chaotic if there exists some additional source in the space-time. Motivated by accreting black holes in astrophysics, we have studied the geodesic dynamics in the field of a Schwarzschild black hole encircled by a thin disc or a ring (see [1] for the last paper of our series devoted to this topic). Hitherto, we restricted the problem to the static and axisymmetric case. However, accreting astrophysical systems tend to rotate rapidly, so it is desirable to release the staticity restriction and extend to the stationary setting. Interestingly, several studies already made in the literature indicate that rotational dragging might attenuate the geodesic chaos. We plan to check this observation using the metric describing the linear perturbation of Schwarzschild due to a rotating light finite thin disc [2]. A related problem might also be studied whether the chaos observed is not mainly induced by crossings of the (thin, thus non-smooth) disc by the geodesics. Still another possibility would be to employ another methods (not yet considered), as e.g. the one based on the analysis of the character of “basin boundaries”. Finally, more analytical work could be done on the perturbation metric itself, mainly the latter should be compared with other solutions describing black holes surrounded by matter. |