  We study asymptotically flat black holes with massive graviton hair within
the ghost-free bigravity theory. There have been contradictory statements in
the literature about their existence -- such solutions were reported some time
ago, but later a different group claimed the Schwarzschild solution to be the
only asymptotically flat black hole in the theory. As a result, the controversy
emerged. We have analyzed the issue ourselves and have been able to construct
such solutions within a carefully designed numerical scheme. We find that for
given parameter values there can be one or two asymptotically flat hairy black
holes in addition to the Schwarzschild solution. We analyze their perturbative
stability and find that they can be stable or unstable, depending on the
parameter values. The masses of stable hairy black holes that would be
physically relevant range form stellar values up to values typical for
supermassive black holes. One of their two metrics is extremely close to
Schwarzschild, while all their "hair" is hidden in the second metric that is
not coupled to matter and not directly seen. If the massive bigravity theory
indeed describes physics, the hair of such black holes should manifest
themselves in violent processes like black hole collisions and should be
visible in the structure of the signals detected by LIGO/VIRGO.
