Do black holes carry scalar hair from spontaneous scalarization?
In plain words
In some theories a black hole becomes surrounded by a cloud of a new scalar field once it is small enough or spins fast enough. This would change how binaries emit gravitational waves.
Precise statement
In scalar-Gauss-Bonnet theories with $f(\phi)$ allowing spontaneous scalarization (Doneva and Yazadjiev 2018; Silva et al. 2018), determine from binary inspirals (dipole radiation entering at $-1$ post-Newtonian order) and ringdowns whether scalarized black holes exist, by constraining the coupling length $\sqrt{\alpha}$ relative to observed black hole masses. An answer is a detection of dipole radiation or a bound on $\sqrt{\alpha}$ that excludes scalarization for all observed masses.
What would settle it
Gravitational-wave constraints on $\sqrt{\alpha}$ below the horizon scale of the lightest observed black holes, or a detection of scalar dipole emission.
Status in the literature
Unverified note
Current bounds on $\sqrt{\alpha}$ from binary inspirals are approximately of order kilometers, leaving scalarization of the lightest black holes allowed as of 2026.