O problema de Hill em relatividade geral / Hill problem in general relativity

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

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

ASSUNTO(S)

problema de lyapunov exponents potenciais pseudo-newtoniana hilll problem post-newtoniana expansão pos-newtoniana poincare fractais pseudo-newtoniana potencials hill expoentes de lyapunov estabilidade seções de poincare stability sections

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