  We present the first study of the dynamical evolution of an isolated star
cluster that combines a significant population of primordial binaries with the
presence of a central black hole. We use equal-mass direct N-body simulations,
with N ranging from 4096 to 16384 and a primordial binary ratio of 0-10%; the
black hole mass is about one percent of the total mass of the cluster. The
evolution of the binary population is strongly influenced by the presence of
the black hole, which gives the cluster a large core with a central density
cusp. Starting from a variety of initial conditions (Plummer and King models),
we first encounter a phase, that last approximately 10 half-mass relaxation
times, in which binaries are disrupted faster compared to analogous simulations
without a black hole. Subsequently, however, binary disruption slows down
significantly, due to the large core size. The dynamical interplay between the
primordial binaries and the black hole thus introduces new features with
respect to the scenarios investigated so far, where the influence of the black
hole and of the binaries have been considered separately. A large core to half
mass radius ratio appears to be a promising indirect evidence for the presence
of a intermediate-mass black hole in old globular clusters.
