  The recent gravitational wave measurements have demonstrated the existence of
stellar mass black hole binaries. It is essential for our understanding of
massive star evolution to identify the contribution of binary evolution to the
formation of double black holes. A promising way to progress is investigating
the progenitors of double black hole systems and comparing predictions with
local massive star samples such as the population in 30 Doradus in the Large
Magellanic Cloud (LMC). Methods. To this purpose, we analyse a large grid of
detailed binary evolution models at LMC metallicity with initial primary masses
between 10 and 40 Msun, and identify which model systems potentially evolve
into a binary consisting of a black hole and a massive main sequence star. We
then derive the observable properties of such systems, as well as peculiarities
of the OB star component. We find that about 3% of the LMC late O and early B
stars in binaries are expected to possess a black hole companion, when assuming
stars with a final helium core mass above 6.6 M to form black holes. While the
vast majority of them may be X-ray quiet, our models suggest that these may be
identified in spectroscopic binaries, either by large amplitude radial velocity
variations ( > 50 km s ) and simultaneous nitrogen surface enrichment, or
through a moderate radial velocity ( > 10 km/s ) and simultaneously rapid
rotation of the OB star. The predicted mass ratios are such that main sequence
companions could be excluded in most cases. A comparison to the observed OB+WR
binaries in the LMC, Be/X-ray binaries, and known massive BH binaries supports
our conclusion. We expect spectroscopic observations to be able to test key
assumptions in our models, with important implications for massive star
evolution in general, and for the formation of double-black hole mergers in
particular.
