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We study the instability of Schwarzschild black holes and the appearance ofscalarized solutions in Einstein-scalar-Gauss-Bonnet gravity performing atime-domain analysis in a perturbative scheme. First we consider a quadraticcoupling function and we perform an expansion for a small perturbation of thescalar field around the Schwarzschild solution up to the second order; we donot observe any stable scalarized configuration, in agreement with previousstudies. We then consider the cases of quartic and exponential coupling, usingan expansion for small values of the Newton's constant, in order to include thenonlinear terms introduced by the coupling in the field equations; in this casewe observe the appearance of stable scalarized solutions different from thosefound in literature. The discrepancy can be an artifact of the perturbativeapproach.

Instability of Schwarzschild Black Holes in Einstein-scalar-Gauss-Bonnet Gravity: Perturbative Approach and Time-Domain Analysis