Extended Gravity and Black Hole Shadows: Rotation Accounting

We obtain black hole rotating solutions for Horndesky theory (specific partial case), bumblebee model and Gauss-Bonnet scalar gravity using the specially improved Newman-Janis algorithm. The shadow profiles for these metrics were calculated. Applying the limitations from the Event Horizon Telescope we find the opportunity to constrain model parameters from considered extended gravity theories. We show that for three considered models two of them (Horndesky theory and Gauss-Bonnet scalar gravity) weaken the effect of rotation and bumblebee model enhances it. This conclusion matches the previously obtained one that extended gravity theories by themselves correct the effect of rotation in both directions.