We present results of numerical simulations of sequences of binary-single scattering events of black holes in dense stellar environments .
The simulations cover a wide range of mass ratios from equal mass objects to 1000:10:10 ~ { } M _ { \odot } and compare purely Newtonian simulations to simulations in which Newtonian encounters are interspersed with gravitational wave emission from the binary .
In both cases , the sequence is terminated when the binary ’ s merger time due to gravitational radiation is less than the arrival time of the next interloper .
We find that black hole binaries typically merge with a very high eccentricity ( 0.93 \leq e \leq 0.95 pure Newtonian ; 0.85 \leq e \leq 0.90 with gravitational wave emission ) and that adding gravitational wave emission decreases the time to harden a binary until merger by \sim 30 to 40 \% .
We discuss the implications of this work for the formation of intermediate-mass black holes and gravitational wave detection .