Extended Gravity and Black Hole Shadows: Rotation Accounting

The first images of the shadows of black holes have opened up new possibilities for testing extended theories of gravity. Using the Newman–Janis method, metrics with rotation for the $$R + {{R}^{2}}$$ model with quantum field corrections are obtained. We have shown that not all previously obtained solutions are consistent with the experimental results of the Event Horizon Telescope. So the more accurate variant to select extended theories of gravity based on black hole rotation taking into account is proposed.