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. Our approach would be also useful for studying the Kozai-Lidov
mechanism in various astrophysical contexts.
