  We estimate the population of black holes with luminous stellar companions
(BH-LCs) in the Milky Way (MW) observable by Gaia. We evolve a realistic
distribution of BH-LC progenitors from zero-age to the current epoch taking
into account relevant physics, including binary stellar evolution, BH-formation
physics, and star formation rate, to estimate the BH-LC population in the MW
today. We predict that Gaia will discover between 3800 and 12,000 BH-LCs by the
end of its 5 yr mission, depending on BH natal kick strength and observability
constraints. We find that the overall yield, and distributions of
eccentricities and masses of observed BH-LCs can provide important constraints
on the strength of BH natal kicks. Gaia-detected BH-LCs are expected to have
very different orbital properties compared to those detectable via radio,
X-ray, or gravitational wave observations.
