ИСТИНА

In a case to explain such unresolved modern phenomena as dark energy, dark matter, processes in the early Universe it seems perspective to extend the theory of general relativity (GR). The next step is to find the physical interpretation for new terms (the cosmological constant, additional fields) in the gravitational action. There are different ways to do this, for example, to extend the consideration to the additional space-time dimensions. All these GR extensions contain new space-time metrics and new solutions. We discuss the idea to use modern extended gravity theories to model the shadows of black holes as their images were obtained not so long ago by the Event Horizon Telescope (EHT). We check the predictions from Horndesky theory, loop quantum gravity, bumblebee and Gauss-Bonnet scalar gravity model, conformal gravity, symmetric tele-parallel equivalent of GR (STEGR) f(Q) gravity in comparison with EHT data. Recently it was demonstrated that both black holes: Sgr A and M87 are rotating. As the direct solving of the Einstein equations with axially-symmetric ansatz represents not very easy task we discuss the Newman-Janis algorithm and its new modifications. Using this method few versions of spinning black hole solutions are obtained. These new metrics are used to constrain modern extended gravity theories using modern astrophysical data on black hole images.