We derive the observable gravitational wave ( GW ) peak frequency ( f ) distribution of binary black holes ( BBHs ) that currently reside inside their globular clusters ( GCs ) , with and without 2.5 Post-Newtonian ( 2.5PN ) effects included in the dynamical evolution of the BBHs .
Recent Newtonian studies have reported that a notable number of nearby non-merging BBHs , i.e .
those BBHs that are expected to undergo further dynamical interactions before merger , in GCs are likely to be observable by LISA .
However , our 2.5PN calculations show that the distribution of \log f for the non-merging BBH population above \sim 10 ^ { -3.5 } Hz scales as f ^ { -34 / 9 } instead of the f ^ { -2 / 3 } scaling found in the Newtonian case .
This leads to an approximately two-orders-of-magnitude reduction in the expected number of GW sources at \sim 10 ^ { -3 } Hz , which lead us to conclude that observing nearby BBHs with LISA is not as likely as has been claimed in the recent literature .
In fact , our results suggest that it might be more likely that LISA detects the population of BBHs that will merge before undergoing further interactions .
This interestingly suggests that the BBH merger rate derived from LIGO can be used to forecast the number of nearby LISA sources , as well as providing insight into the fraction of BBH mergers forming in GCs .