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 ( \sim 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 ^ { -1 } , 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 ( 63 ) .
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 \sim 1000 km s ^ { -1 } are generated intermittently in extremely radial orbits .