Shadow structure of generalized $k-n$ black-bounce metrics

Abstract: The existence of black hole shadows is one of the most interesting effects of the strong field regime of general relativity (GR). Recent observations by the Event Horizon Telescope (EHT) have provided high-resolution images of the vicinity of supermassive black holes, ushering in a new era for testing gravitation on astrophysical scales. In this work, we continue the investigation initiated by \cite{furtado2025gravitational}, focusing on shadows associated with generalized $k-n$ \emph{black-bounce} type spacetimes, which smoothly interpolate between regular black holes and wormholes. We consider a generalization of the metric with free parameters $(a,k,n)$ that modify the mass function and enrich the possible phenomenology. We develop a semi-analytical study of photon orbits, obtaining the critical impact parameter and the shadow radius for different parameter combinations. Subsequently, we perform numerical ray-tracing simulations using the \textsc{GYOTO} code, incorporating optically thick accretion disks and varying the observation angle. Our results reveal characteristic signatures, including the formation of double-ring structures and deformations of the shadow radius, which can serve as observational discriminators between classical black holes and \emph{black-bounce} solutions.