Abstract
We take into account the dynamics of a complete third post-Newtonian conservative Hamiltonian of two spinning black holes, where the orbital part arrives at the third post-Newtonian precision level and the spin-spin part with the spin-orbit part includes the leading-order and next-to-leading-order contributions. It is shown through numerical simulations that the next-to-leading order spin-spin couplings play an important role in chaos. A dynamical sensitivity to the variation of single parameter is also investigated. In particular, there are a number of \textit{observable} orbits whose initial radii are large enough and which become chaotic before coalescence.
Highlights
Massive binary black-hole systems are likely the most promising sources to be used for future gravitational wave detectors
Levin [18] thought that there is no formal conflict between them since the two approaches are not exactly but approximately equal, and different dynamical behaviors between the two approximately related systems are permitted according to the dynamical system theory
Any PN conservative Hamiltonian binary system with one body spinning and a conservative Hamiltonian of two bodies spinning without the constraint of equal mass are still integrable
Summary
Massive binary black-hole systems are likely the most promising sources to be used for future gravitational wave detectors. An extremely sensitive dependence on initial conditions as the basic feature of chaotic systems would pose a challenge to the implementation of such matched filters, since the number of filters required to detect these waveforms is exponentially large with increasing detection sensitivity This has led some authors to focus on research of chaos in the orbits of two spinning black holes. For the sake of this, we shall consider a complete 3PN conservative Hamiltonian of two spinning black holes, where the orbital part is up to the 3PN order and the spin–spin part as well as the spin–orbit part includes the LO and NLO interactions In this way, we want to know whether the inclusion of the NLO spin–spin couplings has an effect on chaos, and whether there is chaos before the coalescence of the binaries
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