  In general relativity, all vacuum black holes are described by the Kerr
solution. Beyond general relativity, there is a prevailing expectation that
deviations from the Kerr solution increase with the horizon curvature. We
challenge this expectation by showing that, in a scalar-Gauss-Bonnet theory,
black holes scalarize in a finite, adjustable window of black-hole masses,
bounded from above and below. In this theory, there is an interplay between
curvature scales and compactness, which we expect to protect neutron stars and
other less compact objects from scalarization. In particular, black-hole
uniqueness can be broken at supermassive black-hole scales, while solar-mass
black holes remain well-described by the Kerr solution. To probe this scenario,
observations targeting supermassive black holes are necessary.
