Astrophysical Tests of General Relativity

At the initial stage of its development, general relativity (GR) was verified and confirmed in a weak gravitational field limit. However, with the development of astronomical observation technologies, GR predictions in a strong gravitational field began to be discussed and confirmed, such as the profile of the X-ray iron \(K\alpha \) line (in the case if the emission region is very close to the event horizon), the trajectories of stars near black holes and the shapes and sizes of shadows of supermassive black holes in M87* and Sgr A*. In 2005 it was predicted that a shadow formed near a supermassive black hole at the Galactic Center could be reconstructed from observations of ground based global VLBI system or ground—space interferometer acting in mm or sub-mm bands. In 2022 this prediction was confirmed since the Event Horizon Telescope (EHT) collaboration reported about a shadow reconstructions for Sgr A*. In 2019 the EHT collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87. In 2021 the EHT collaboration constrained parameters (“charges”) of spherical symmetrical metrics of black holes from an allowed interval for shadow radius. In 2022 the EHT collaboration constrained charges of metrics for the supermassive black hole at the Galactic Center. Earlier, we obtained analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner–Nordström metric. Based on results of the shadow size evaluation for M87* done by the EHT collaboration we constrained a tidal charge. We discussed opportunities to use shadows to test alternative theories of gravity and alternative models for galactic centers.