Spin stability of a binary black hole coalescence

Abstract

We analyze the spin stability of a binary black hole coalescence when the binary system is described by the Post-Newtonian (PN) equations in the adiabatic regime. The main idea in this work is to make a massive exploration of the solution space in search of chaos. For that, we evolve the PN equations using a CUDA implementation of the RKF78 scheme and study the dynamical behavior of the system. Each initial spin configuration run in the GPU is composed by more than 80000 simulations. The chaos indicator used to characterize the degree of separation of two infinitesimally close trajectories is the Lyapunov exponent. We find zones in the solution space where the separation between nearby trajectories reaches several orders of magnitude bigger than the initial separation. Also, we note that the chaotic behavior can be observed in forward as well as in backward evolution.