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

## TL;DR

This paper demonstrates through numerical simulations that a Schwarzschild black hole can develop scalar hair from a time-varying scalar field, with implications for scalar-tensor theories and dark matter models.

## Contribution

It shows that a non-trivial scalar field profile can grow around a Schwarzschild black hole under specific initial conditions, expanding understanding of black hole scalar hair formation.

## Key findings

- Scalar hair can grow on Schwarzschild black holes with time-varying scalar backgrounds.
- The scalar hair development timescale relates to the black hole mass and scalar mass.
- Qualitative features are consistent with and without backreaction on the metric.

## Abstract

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.