  We study the evolution of a massive scalar field surrounding a Schwarzschild
black hole and find configurations that can survive for arbitrarily long times,
provided the black hole or the scalar field mass is small enough. In
particular, both ultra-light scalar field dark matter around supermassive black
holes and axion-like scalar fields around primordial black holes can survive
for cosmological times. Moreover, these results are quite generic, in the sense
that fairly arbitrary initial data evolves, at late times, as a combination of
those long-lived configurations.
