  Now that LIGO has revealed the existence of a large number of binary black
holes, identifying their origin becomes an important challenge. They might
originate in more isolated regions of the galaxy or alternatively they might
reside in dense environments such as galactic centers or globular clusters. In
the latter case, their center of mass motion as well as their orbital
parameters should lead to observable changes in the waveforms, which would
reflect their gravitational interactions with the surrounding matter. This
would be reflected in the gravitational wave signal by a net phase change or
even a time-dependent Doppler shift. We show that this time-dependence might be
observable in future space gravitational wave detectors such as LISA which
could provide direct information about the black hole binary environments and
otherwise invisible ambient mass.
