Eccentricity boost of stars around shrinking massive black hole binaries

Based on a simple geometrical approach, we analyze the evolution of the Kozai-Lidov mechanism for stars around shrinking massive black hole binaries on circular orbits. We find that, due to a peculiar bifurcation pattern induced by the Newtonian potential of stellar clusters, the orbit of stars could become highly eccentric. This transition occurs abruptly for stars with small initial eccentricities. The approach presented in this paper may be useful for studying the Kozai-Lidov mechanism in various astrophysical contexts.