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In the present letter we show the existence of a fully nonlinear dynamicalmechanism for the formation of scalarized black holes which is different fromthe spontaneous scalarization. We consider a class of scalar-Gauss-Bonnetgravity theories within which no tachyonic instability can occur. Although theSchwarzschild black holes are linearly stable against scalar perturbations, weshow dynamically that for certain choices of the coupling function they areunstable against nonlinear scalar perturbations. This nonlinear instabilityleads to the formation of new black holes with scalar hair. The fully nonlinearand self-consistent study of the equilibrium black holes reveals that thespectrum of solutions is more complicated and more than one scalarized branchcan exist. We have also considered classes of scalar-Gauss-Bonnet theorieswhere both the standard and the nonlinear scalarization can be present, andthey are smoothly connected that completes in an interesting way the picture ofblack hole scalarization. The fully nonlinear (de)scalarization of aSchwarzschild black hole will always happen with a jump because the stable"scalarized branch" is not continuously connected to the Schwarzschild one thatcan leave clear observational signatures.

Beyond the spontaneous scalarization: New fully nonlinear dynamical mechanism for formation of scalarized black holes