Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-08-23
Phys.Rev.D84:104038,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages, 17 figures and 4 tables. Version published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1012.4423
Scientific paper
10.1103/PhysRevD.84.104038
We study the stability and chaos of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner-Hamiltonian formulation. We include terms up to 2.5 PN order in the orbital part and the leading order in spin corrections. We performed numerical simulations of a hierarchical configuration of three compact bodies in which a binary system is perturbed by a third, lighter body initially positioned far away from the binary. The relative importance of the different PN orders is examined. The basin boundary method and the computation of Lyapunov exponent were employed to analyze the stability and chaotic properties of the system. The 1 PN terms produced a small but noticeable change in the stability regions of the parameters considered. The inclusion of spin or gravitational radiation does not produced a significant change with respect to the inclusion of the 1 PN terms.
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