In the present paper, we show the existence of a fully nonlinear mechanism for the formation of scalarized black holes, which is different from the spontaneous scalarization, and demonstrate its dynamical development. We consider a class of scalar-Gauss-Bonnet gravity theories within which no tachyonic instability can occur. Although the Schwarzschild black holes are linearly stable against scalar perturbations, we show dynamically that for certain choices of the coupling function, they are unstable against nonlinear scalar perturbations. This nonlinear instability leads to the formation of new black holes with scalar hair. The fully nonlinear and self-consistent study of the equilibrium black holes reveals that the spectrum of solutions is more complicated and more than one scalarized branch can exist. We have also considered classes of scalar-Gauss-Bonnet theories where both the standard and the nonlinear scalarization can be present, and they are smoothly connected that completes in an interesting way the picture of black hole scalarization. The fully nonlinear (de)scalarization of a Schwarzschild black hole will always happen with a jump because the stable “scalarized branch” is not continuously connected to the Schwarzschild one that can leave clear observational signatures.

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• Alternative gravity theories
• Classical black holes