Shadows from spinning black holes in extended gravity

When the the shadow image of a supermassive black hole in the center of M87 was obtained a new era in the observational astrophysics began. The resolution improvement would allow to test extended gravity models at event horizon scales. We develop the method allowing to take into account the black hole rotation in black hole shadow modelling. It is demonstrated that the shadow of a black hole with a diameter smaller than $4R_{Sw}$ ($R_{Sw} = 2M$) cannot be represented in the terms of pure Kerr-Newman metric. Therefore, the detection of a shadow of such size would indicate that further expansions must be taken into account. This fact could give new indications on the detailed form of the theory of gravity at the considered scales.}