Kluitenberg, Martijn (2021) Chaotic scattering in relativistic N-center problems. Master's Thesis / Essay, Mathematics.
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Abstract
We study relativistic systems with $N$ static black holes in the Einstein-Maxwell-dilaton theory of gravitation. There is an arbitrary coupling constant $a$ for the dilaton. Unlike in classical mechanics, the relativistic 2-center problem seems to be chaotic for values of $a$ between 0 and $\sqrt{3}$. For this latter value of $a$, the system is integrable, like in the classical case. We prove rigorously - using methods from potential scattering - that the motion of light in problems with 3 or more centers is chaotic for a discrete set of $a$'s between 1 and $\sqrt{3}$. The value $a = 1$ is a turning point, where the qualitative features of the black holes change.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 14 Jul 2021 12:30 |
| Last Modified: | 14 Jul 2021 12:30 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25238 |
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