1108.4485 (Pablo Galaviz)

Stability and chaos of hierarchical three black hole configurations    [PDF]

Pablo Galaviz

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.

View original: http://arxiv.org/abs/1108.4485