Echoes and quasinormal modes of asymmetric black bounces

Abstract

We study quasinormal modes and echoes of symmetric and asymmetric black bounce solutions generated by anisotropic fluids within the framework of general relativity. We derive the effective potential governing massless scalar fields and compute the corresponding quasinormal mode spectra using three independent methods: sixth-order WKB, P\"oschl-Teller and time-domain evolution. Our results show that symmetric black bounce configurations with horizons yield a standard single-barrier potential, while horizonless solutions may exhibit multiple potential barriers that generate gravitational wave echoes. These echoes are sensitive to model parameters such as the fluid energy density and the regularizing parameter $a$ that defines the minimal $2$-sphere. The asymmetric models considered recover the Reissner-Nordstr\"om solution in their external region but can be bounded or unbounded in the inside, depending on the sign of a parameter. Both cases have similar qualitative properties as far as wave emission is concerned but show no echoes. This makes it very difficult to distinguish them from standard Reissner-Nordstr\"om configurations.