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We study the axial quasinormal modes of hairy black holes in Gauss-Bonnetgravity with massive self-interacting scalar field. Two coupling functions ofthe scalar field to the Gauss-Bonnet invariant are adopted with one of themleading to black hole scalarization. The axial perturbations are studied viatime evolution of the perturbation equation, and the effect of the scalar fieldmass and the self-interaction constant on the oscillation frequency and dampingtime is examined. We study as well the effect of nonzero scalar field potentialon the critical point at which the perturbation equation loses hyperbolicity inthe case of black hole scalarization. The results show that the non-zero scalarfield potential extends the range of parameters where such loss ofhyperbolicity is observed thus shrinking the region of stable black holeexistence. This will have an important effect on the nonlinear dynamicalsimulation studies in massive scalar Gauss-Bonnet gravity.

Axial perturbations of hairy Gauss-Bonnet black holes with massive self-interacting scalar field