Rocco D'Agostino, Vittorio De Falco

We present a comprehensive study of the quasinormal modes of a new class of nonlocal static and spherically symmetric black hole (BH) solutions within the framework of the revised Deser-Woodard theory of gravity. These solutions are constructed as linear perturbations of the Schwarzschild spacetime and are characterized by an inverse power-law behavior of the lapse metric function. We derive the radial profiles of the effective potentials corresponding to scalar, electromagnetic and axial gravitational fluctuations on the BH background. Using the WKB method, complemented by Pad\'e approximants to regularize the trend of the effective potential near its peak, we compute the complex quasinormal mode frequencies associated with each type of perturbation. Our results are examined from both mathematical and physical perspectives, and are substantiated with references to existing literature. In particular, we compare the numerical outcomes with the predictions of the Schwarzschild metric to quantify deviations from the framework of general relativity. When all types of perturbations are combined, the relative deviations of the fundamental modes can reach up to $\sim 12\%$. Finally, we discuss the possibility to place observational bounds in the BH parameter space, based on the predicted sensitivities of future gravitational wave detectors.