Relativistic encounters in dense stellar systems
  Two coalescing black holes (BHs) represent a conspicuous source of
gravitational waves (GWs). The merger involves 17 parameters in the general
case of Kerr BHs, so that a successful identification and parameter extraction
of the information encoded in the waves will provide us with a detailed
description of the physics of BHs. A search based on matched-filtering for
characterization and parameter extraction requires the development of some
$10^{15}$ waveforms. If a third additional BH perturbed the system, the
waveforms would not be applicable, and we would need to increase the number of
templates required for a valid detection. In this letter, we calculate the
probability that more than two BHs interact in the regime of strong relativity
in a dense stellar cluster. We determine the physical properties necessary in a
stellar system for three black holes to have a close encounter in this regime
and also for an existing binary of two BHs to have a strong interaction with a
third hole. In both cases the event rate is negligible. While dense stellar
systems such as galactic nuclei, globular clusters and nuclear stellar clusters
are the breeding grounds for the sources of gravitational waves that
ground-based detectors like Advanced LIGO and Advanced VIRGO will be exploring,
the analysis of the waveforms in full general relativity needs only to evaluate
the two-body problem. This reduces the number of templates of waveforms to
create by orders of magnitude.
