Relaxation rate of ModMax–de Sitter black holes perturbed by massless neutral scalar fields

In this study, we investigate the behavior of ModMax-de Sitter black holes when perturbed by massless neutral scalar fields. Specifically, we analyze how the relaxation time, defined as the inverse of the fundamental imaginary frequency, varies with respect to two key parameters: the cosmological constant and the nonlinear parameter characterizing the ModMax theory. We explore scenarios both with and without a cosmological constant, focusing on the static charged ModMax black hole configuration. Our results reveal dependencies between the relaxation time and the nonlinear parameter, shedding light on the dynamical properties of these black hole systems. We also show the validity of WKB approximation under consideration.