Schwarzschild black holes can wear scalar wigs
  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. 
Juan Barranco, Argelia Bernal, Juan Carlos Degollado, Alberto   Diez-Tejedor, Miguel Megevand, Miguel Alcubierre, Dar\'io N\...
gr-qc astro-ph.CO hep-th