Merger Criteria of Multiple Massive Black Holes and the Impact on the
  Host Galaxy
  We perform N-body simulations on a multiple massive black hole (MBH) system
in a host galaxy to derive the criteria for successive MBH merger. The
calculations incorporate the dynamical friction by stars and general
relativistic effects as pericentre shift and gravitational wave recoil. The
orbits of MBHs are pursed down to ten Schwarzschild radii (~ 1 AU). As a
result, it is shown that about a half of MBHs merge during 1 Gyr in a galaxy
with mass $10^{11}M_{\odot}$ and stellar velocity dispersion 240 km/s, even if
the recoil velocity is two times as high as the stellar velocity dispersion.
The dynamical friction allows a binary MBH to interact frequently with other
MBHs, and then the decay of the binary orbits leads to the merger through
gravitational wave radiation, as shown by Tanikawa & Umemura (2011). We derive
the MBH merger criteria for the masses, sizes, and luminosities of host
galaxies. It is found that the successive MBH mergers are expected in bright
galaxies, depending on redshifts. Furthermore, we find that the central stellar
density is reduced by the sling-shot mechanism and that high-velocity stars
with ~ 1000 km/s are generated intermittently in extremely radial orbits.
