  If binaries consisting of two 100 Msun black holes exist they would serve as
extraordinarily powerful gravitational-wave sources, detectable to redshifts of
z=2 with the advanced LIGO/Virgo ground-based detectors. Large uncertainties
about the evolution of massive stars preclude definitive rate predictions for
mergers of these massive black holes. We show that rates as high as hundreds of
detections per year, or as low as no detections whatsoever, are both possible.
It was thought that the only way to produce these massive binaries was via
dynamical interactions in dense stellar systems. This view has been challenged
by the recent discovery of several stars with mass above 150 Msun in the R136
region of the Large Magellanic Cloud. Current models predict that when stars of
this mass leave the main sequence, their expansion is insufficient to allow
common envelope evolution to efficiently reduce the orbital separation. The
resulting black-hole--black-hole binary remains too wide to be able to coalesce
within a Hubble time. If this assessment is correct, isolated very massive
binaries do not evolve to be gravitational-wave sources. However, other
formation channels exist. For example, the high multiplicity of massive stars,
and their common formation in relatively dense stellar associations, opens up
dynamical channels for massive black hole mergers (e.g., via Kozai cycles or
repeated binary-single interactions). We identify key physical factors that
shape the population of very massive black-hole--black-hole binaries. Advanced
gravitational-wave detectors will provide important constraints on the
formation and evolution of very massive stars.
