Abstract
A relativistic approach of the Hill Problem is presented by using an approximate binary system metric obtained from the first post-Newtonian expansion (1PN). We employ Poincaré maps and Lyapunov exponents to study the stability of bounded orbits of the system for different mass arrangements, and compare with the classical problem based on Newtonian dynamics. We find that for larger masses the system become totally stable, a striking behaviour that is not predicted by the Newtonian dynamics.
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