Emerging black hole shadow from collapsing boson star

This work devotes to investigate the dynamical emergence of black hole shadow from gravitational lensing in dynamical spacetime by using the collapsing boson star. Two characterized scenarios are adopted with or without considering the time delay of light propagation. As the boson star evolves, new Einstein rings emerge from the lensing center, with their radius gradually increasing, and their number continues to grow infinitely before the light-ring forms. The shadow forms instantaneously at the moment the black hole appears when ignoring the time delay of light propagation. Considering the time delay for light propagation in dynamical spacetime, a more intricate process of the shadow formation is uncovered: it first appears as a minute dot in the lensing center, then gradually grows as the black hole grows, eventually expands the inner region of the light-ring. During the quasi-stable phases of boson star and black hole, the lensing and shadow structures from two scenarios are nearly identical and remain almost unchanged. Our results present the universal dynamic patterns of the lensing and shadow structures, and reveal the potential observed phenomena near the collapsing star and the event horizon of the newly formed black hole.