Galaxies with Supermassive Binary Black Holes: (I) A Possible Model for
  the Centers of Core Galaxies
  The dynamics of galactic systems with central binary black holes is studied.
The model is a modification from the restricted three body problem, in which a
galactic potential is added as an external potential. Considering the case with
an equal mass binary black holes, the conditions of existence of equilibrium
points, including Lagrange Points and additional new equilibrium points, i.e.
Jiang-Yeh Points, are investigated. A critical mass is discovered to be
fundamentally important. That is, Jiang-Yeh Points exist if and only if the
galactic mass is larger than the critical mass. The stability analysis is
performed for all equilibrium points. The results that Jiang-Yeh Points are
unstable could lead to the core formation in the centers of galaxies.
