# Black Hole Hair from Scalar Dark Matter

## TL;DR

This paper demonstrates that scalar dark matter can form scalar hair around black holes, with the profile depending on the scalar mass, providing potential observational signatures related to dark matter particle properties.

## Contribution

It generalizes Jacobson's scalar hair phenomenon to oscillating massive scalars, exploring scalar profiles around black holes for different masses and implications for dark matter detection.

## Key findings

- Scalar hair develops around black holes due to scalar dark matter.
- Scalar profile varies with mass, showing different radial dependencies.
- Potential observational signatures near supermassive black holes like M87.

## Abstract

We show that a black hole surrounded by scalar dark matter develops scalar hair. This is the generalization of a phenomenon pointed out by Jacobson, that a minimally coupled scalar with a non-trivial time dependence far away from the black hole would endow the black hole with hair. In our case, the time dependence arises from the oscillation of a scalar field with a non-zero mass. We systematically explore the scalar profile around the black hole for different scalar masses. In the small mass limit, the scalar field has a $1/r$ component at large radius $r$, consistent with Jacobson's result. In the large mass limit (with the Compton wavelength of order of the horizon or smaller), the scalar field has a $1/r^{3/4}$ profile yielding a pile-up close to the horizon, while distinctive nodes occur for intermediate masses. Thus, the dark matter profile around a black hole, while challenging to measure, contains information about the dark matter particle mass. As an application, we consider the case of the supermassive black hole at the center of M87, recently imaged by the Event Horizon Telescope. Its horizon size is roughly the Compton wavelength of a scalar particle of mass $10^{-20}$ eV. We consider the implications of the expected scalar pile-up close to the horizon, for fuzzy dark matter at a mass of $10^{-20}$ eV or below.