Researchers show that fast rotation alone can spur a black hole to grow a nontrivial scalar field, even when the ordinary linear trigger for such growth is absent. The work studies a version of Einstein-scalar-Gauss-Bonnet (EsGB) gravity, a theory that adds a single extra scalar field and a special curvature term (the Gauss–Bonnet invariant) to Einstein’s equations. By choosing a coupling between the scalar and curvature that removes the usual linear instability, the authors isolate a genuinely nonlinear route to “scalarization”—the appearance of scalar hair around a rotating (Kerr) black hole.

The team first held the spacetime geometry fixed and evolved the scalar field on a Kerr black hole background. They found that sufficiently rapid rotation alters the Gauss–Bonnet invariant near the horizon so that a negative region appears close to the poles. For negative values of the coupling parameter used in the study, this negative region acts like a geometric trapping zone and creates an effective potential that can support nonlinear growth of the scalar field. The authors identify a clear threshold in dimensionless spin, χ = 0.5: below that value no trapping region forms near the poles, while above it the region appears and can support growth.

Because their coupling was chosen so that small perturbations are governed by the ordinary massless wave equation, there is no linear, or “tachyonic,” instability of the bald Kerr solution. In practice this means whether scalar hair grows depends on the size of the initial perturbation. In time-evolution examples on fixed backgrounds, low-spin cases saw all perturbations decay back to zero. For high-spin cases (χ above 0.5), sufficiently large initial wavepackets led to sustained growth and saturation of the scalar field, demonstrating a nonlinear scalarization process that requires a finite perturbation to get started.