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# Chaotic scattering in relativistic N-center problems

Kluitenberg, Martijn (2021) Chaotic scattering in relativistic N-center problems. Master's Thesis / Essay, Mathematics.

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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.