Remarks on nonperturbative perturbations

We consider the linearized perturbations of near-horizon extremal Reissner-Nordström black holes in d-dimensional Einstein-Maxwell-Gauss-Bonnet gravity and seven-dimensional third-order Lovelock gravity. We find the solutions for the gravitational perturbations as a function of the higher-derivative coupling coefficients, which we treat nonperturbatively. Consequently, we observe a breakdown in perturbation theory for large harmonics for the six-derivative corrections.