On the growth of massive scalar hair around a Schwarzschild black hole

Through numerical simulations of a minimally coupled massive Klein-Gordon scalar field, we show that it is possible to grow hair on a Schwarzschild black hole if one assumes an initial periodically time-varying but spatially homogeneous scalar background. By "hair", we mean a non-trivial profile in the scalar field. We find that this profile emerges on a timescale related to the mass of the black hole, with features related to the mass of the scalar particle. We undertake simulations with and without backreaction on the metric and see that the essential, qualitative features remain consistent. We also contrast the results from higher mass scalars to the case of a low mass with a large Compton wavelength. The results are particularly relevant for scalar-tensor theories of gravity and dark matter models consisting of a massive scalar, e.g. axions.
Comment: 9 pages, 8 figures, updated to incorporate low mass cases and referee suggestions