Black hole scalar hair grows unbounded in an expanding universe

In a theory where a scalar field couples to spacetime curvature via the Gauss-Bonnet term, black holes acquire a 'hair' — a surrounding scalar field profile. Tracking this hair in de Sitter spacetime reveals it grows both in time and across superhorizon distances, mirroring the behavior of any minimally coupled massless scalar in an expanding universe. Even a simple point charge reproduces the same growth, so the black hole acts merely as a localized source, not the cause of the instability. The hair also carries a steady outward energy flux, explaining why static self-consistent solutions in this theory have proven so difficult to construct.