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

We study the axial quasinormal modes of hairy black holes in Gauss-Bonnet gravity with massive self-interacting scalar field. Two coupling functions of the scalar field to the Gauss-Bonnet invariant are adopted with one of them leading to black hole scalarization. The axial perturbations are studied via time evolution of the perturbation equation, and the effect of the scalar field mass and the self-interaction constant on the oscillation frequency and damping time is examined. We study as well the effect of nonzero scalar field potential on the critical point at which the perturbation equation loses hyperbolicity in the case of black hole scalarization. The results show that the non-zero scalar field potential extends the range of parameters where such loss of hyperbolicity is observed thus shrinking the region of stable black hole existence. This will have an important effect on the nonlinear dynamical simulation studies in massive scalar Gauss-Bonnet gravity.