Stability and chaos of hierarchical three black hole configurations

TL;DR

This paper investigates the stability and chaotic behavior of a hierarchical three-body system with compact objects using post-Newtonian equations, highlighting the effects of different PN orders and spin corrections on system dynamics.

Contribution

It provides a detailed numerical analysis of how various post-Newtonian terms influence the stability and chaos in hierarchical three-black-hole configurations.

Findings

1 PN terms slightly alter stability regions.

Spin and gravitational radiation have minimal impact.

Chaotic behavior assessed via Lyapunov exponents.

Abstract

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.