Investigating the retention of intermediate-mass black holes in star
  clusters using N-body simulations
  Contrary to supermassive and stellar-mass black holes (SBHs), the existence
of intermediate-mass black holes (IMBHs) with masses ranging between 10^{2-5}
Msun has not yet been confirmed. The main problem in the detection is that the
innermost stellar kinematics of globular clusters (GCs) or small galaxies, the
possible natural loci to IMBHs, are very difficult to resolve. However, if
IMBHs reside in the centre of GCs, a possibility is that they interact
dynamically with their environment. A binary formed with the IMBH and a compact
object of the GC would naturally lead to a prominent source of gravitational
radiation, detectable with future observatories. We use N-body simulations to
study the evolution of GCs containing an IMBH and calculate the gravitational
radiation emitted from dynamically formed IMBH-SBH binaries and the possibility
that the IMBH escapes the GC after an IMBH-SBH merger. We run for the first
time direct-summation integrations of GCs with an IMBH including the dynamical
evolution of the IMBH with the stellar system and relativistic effects, such as
energy loss in gravitational waves (GWs) and periapsis shift, and gravitational
recoil. We find in one of our models an intermediate mass-ratio inspiral
(IMRI), which leads to a merger with a recoiling velocity higher than the
escape velocity of the GC. The GWs emitted fall in the range of frequencies
that a LISA-like observatory could detect, like the European eLISA or in
mission options considered in the recent preliminary mission study conducted in
China. The merger has an impact on the global dynamics of the cluster, as an
important heating source is removed when the merged system leaves the GC. The
detection of one IMRI would constitute a test of GR, as well as an irrefutable
proof of the existence of IMBHs.
