Shadow formation in gravitational collapse: redshift and blueshift by spacetime dynamics

A black hole illuminated by a background light source is observed as a black hole shadow. For a black hole formed by the gravitational collapse of a transmissive object, redshift of light due to the spacetime dynamics is expected to play a crucial role in the shadow formation. In this talk, we investigate the redshift of light caused by the spacetime dynamics. First, we consider a spherical shell model. We see that the collapse of a shell typically leads to the redshift of light, while blueshift can be also observed in some cases. This result suggests that a shadow image is generally formed in the late stage of the gravitational collapse of a transmissive object. Second, we consider a general, dynamical, spherically symmetric spacetime and propose a new covariant formula for the redshift of light. This formula relates the dynamical redshift to the energy-momentum tensor of the background spacetime and provides its intuitive interpretation with Newtonian analogy.