Infinite tower of higher-curvature corrections: Quasinormal modes and late-time behavior of $D$-dimensional regular black holes

Recently, Bueno, Cano, and Hennigar [Regular black holes from pure gravity, arXiv:2403.04827.] proposed a generic approach for incorporating an infinite tower of higher-curvature corrections into the Einstein theory. In this study, we compute quasinormal modes for certain regular $D$-dimensional black holes resulting from this infinite series of higher-curvature corrections, specifically focusing on the $D$-dimensional extensions of the Bardeen and Hayward black holes. We demonstrate that while the fundamental mode is minimally affected by moderate coupling constants, the higher overtones exhibit significant sensitivity even to small coupling values, yielding unconventional modes characterized by vanishing real oscillation frequencies. When comparing the frequencies derived from the metric truncated at several orders of higher-curvature corrections with those resulting from the infinite series of terms, we observe a rapid convergence of the frequencies to their limit for the complete regular black hole. This validates the extensive research conducted on specific theories with a finite number of higher-curvature corrections, such as the Lovelock theory.