By performing Monte Carlo simulations of the evolution of binary primordial black hole ( PBH ) systems , we estimate the effect of distant encounters with single PBHs upon the coalescence time and merger rate of binary PBHs .
We find that , for models where PBHs compose a large fraction of dark matter , f _ { \mathrm { PBH } } \sim 1 , the expected fractional change in coalescence time is negligible , of order 10 ^ { -6 } for most binaries .
For models with significantly lower PBH abundances , f _ { \mathrm { PBH } } \ll 1 , we find that the average change in binary lifetime due to encounters can be as large as \mathcal { O } ( 10 ^ { -2 } ) , with a small number of binaries experiencing an order unity change in lifetime .
In the absence of encounters , we also compare the use of an analytic approximation for the coalescence time to numerically evolving the binary system , finding that the analytic approximation results in an order 10 \% error in the coalescence time .
However , when these effects are taken into consideration , there is a negligible change to the calculated merger rate , placing previous constraints on the PBH abundance arising from observed gravitational wave signals from merging binary black holes on a more secure footing .