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Hill problem in general relativity

Author(s):
Andre Fabiano Steklain
Total Authors: 1
Document type: Doctoral Thesis
Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:
Examining board members:
George Emanuel Avraam Matsas; Gilberto Medeiros Kremer; Henrique Pereira de Oliveira; Marcus Aloizio Martinez de Aguiar
Advisor: Patricio Anibal Letelier Sotomayor
Abstract

In this work the Hill problem dynamics is analyzed using two different approaches. In the first approach, still in the realm of Newtonian mechanics, we use potentials that reproduce General Relativity effects. We use the Paczynski-Wiita and one of the Artemova, Bj¨ornsson e Novikov (ABN) potentials. These potentials reproduce effects that arise in the context of the Schwarzschild metric (event horizon) and of the Kerr metric (Lense-Thirring effect), respectively. On the second approach the equations of motion are obtained using general relativity, from the approximate metric of a binary system obtained from post-Newtonian expansions up to first order (1PN). In the analysis of the dynamics we study the stability of bounded orbits using classical tools, like Poincare sections and Lyapunov exponents. We also study open trajectories using Fractal Escape analysis. From our results we remark that two features. For the ABN potential there is an influence of the rotations on the stability of the orbits. In general relativity there is a limit where the system, in general chaotic, become stable, in disagreement with the pseudo-Newtonian potentials, in particular the Paczy´nski-Wiita potential (AU)