Identification of a Regular Black Hole by Its Shadow

We study shadows of regular rotating black holes described by the axially symmetric solutions asymptotically Kerr for a distant observer, obtained from regular spherical solutions of the Kerr-Schild class specified by Ttt=Trr(pr=-epsilon). All regular solutions obtained with the Newman-Janis algorithm belong to this class. Their basic generic feature is the de Sitter vacuum interior. Information about the interior content of a regular rotating de Sitter-Kerr black hole can be in principle extracted from observation of its shadow. We present the general formulae for description of shadows for this class of regular black holes, and numerical analysis for two particular regular black hole solutions. We show that the shadow of a de Sitter-Kerr black hole is typically smaller than that for the Kerr black hole, and the difference depends essentially on the interior density and on the pace of its decreasing.