Shadows and gravitational perturbations of black bounces

Abstract: We investigate axial gravitational perturbations and shadow formation in black-bounce geometries supported by anisotropic fluids within general relativity. Two distinct classes of solutions are analyzed: a symmetric Simpson--Visser-like black bounce and an asymmetric deformation of the Reissner--Nordström metric, which can feature either a bounded interior region or an unbounded wormhole-like extension. Our findings indicate that configurations with horizons, whether symmetric or asymmetric, exhibit single-barrier effective potentials and quasinormal frequencies nearly indistinguishable from those of standard black holes. In contrast, horizonless symmetric configurations may develop multiple potential barriers, giving rise to gravitational-wave echoes whose amplitude and separation depend sensitively on the bounce parameter $a$ and the density parameter $ρ_0$. Horizonless asymmetric solutions, on the other hand, exhibit regularized effective potentials that do not produce echoes and remain phenomenologically close to the Reissner--Nordström case. From the optical perspective, both classes of solutions with horizons exhibit a single relevant photon sphere and shadow profiles nearly indistinguishable from those of their black-hole counterparts, while horizonless symmetric configurations can sustain multiple photon rings. Horizonless asymmetric configurations may instead support either a single photon ring or none. Finally, we recover the standard eikonal correspondence between quasinormal modes and the instability of circular null geodesics for configurations with horizons. For horizonless geometries, however, the emergence of multiple potential barriers prevents a straightforward extension of this relation, although the strong similarity between the wave and optical sectors suggests that a meaningful phenomenological correspondence may still persist.