Shadows near supermassive black holes: from a theoretical concept to GR test

General relativity (GR) passed many astronomical tests but in majority of them GR predictions have been tested in a weak gravitational field approximation. Around 50 years ago a shadow has been introduced by J. Bardeen as a purely theoretical concept but due to an enormous progress in observational and computational facilities this theoretical prediction has been confirmed and the most solid argument for an existence of supermassive black holes in Sgr A* and M87* has been obtained.Comment: 12 pages, 1 figure, presented as a talk at The 6th International Conference on Particle Physics and Astrophysics (ICPPA-2022), accepted in IJMP

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars

As it was pointed out recently in Hees et al. (2017), observations of stars near the Galactic Center with current and future facilities provide an unique tool to test general relativity (GR) and alternative theories of gravity in a strong gravitational field regime. In particular, the authors showed that the Yukawa gravity could be constrained with Keck and TMT observations. Some time ago, Dadhich et al. (2001) showed that the Reissner -- Nordstr\"om metric with a tidal charge is naturally appeared in the framework of Randall -- Sundrum model with an extra dimension ($Q^2$ is called tidal charge and it could be negative in such an approach). Astrophysical consequences of of presence of black holes with a tidal charge are considerered, in particular, geodesics and shadows in Kerr -- Newman braneworld metric are analyzed in (Schee and Stuchlik, 2009a), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in (Schee and Stuchlik, 2009b). Possible observational signatures of gravitational lensing in a presence of the Reissner -- Nordstr\"om black hole with a tidal charge at the Galactic Center are discussed in papers by Bin-Nun (2010a, 2010b, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner -- Nordstrom -- de-Sitter solution in post-Newtonian approximation and discuss opportunities to constrain parameters of the metric from observations of bright stars with current and future astrometric observational facilities such as VLT, Keck, GRAVITY, E-ELT and TMT.Comment: 9 pages, references were added, minor typos were correcte

Shadows around Sgr A* and M87* as a tool to test gravity theories

In the framework of Randall -- Sundrum theory with extra dimension Reissner -- Nordstr\"om black hole solutions with a tidal charge have been found. The shadow around the supermassive black hole in M87 was reconstructed in 2019 based on observations with the Event Horizon Telescope (EHT) in April 2017. In May 2022 the EHT Collaboration presented results of a shadow reconstruction for our Galactic Center. Earlier, for Reissner -- Nordstr\"om metric we derived analytical expressions for shadow size as a function of charge and later generalized these results for a tidal charge case. We discuss opportunities to evaluate parameters of alternative theories of gravity with shadow size estimates done by the EHT Collaboration, in particular, a tidal charge could be estimated from these observations.Comment: 10 pages, 1 figure, presented at the ICRANet-ISFAHAN Astronomy Meeting, accepted in Astronomical and Astrophysical Transactions; typos were correcte

Contribution of microlensing to X-ray variability of distant QSOs

We consider a contribution of microlensing to the X-ray variability of high-redshifted QSOs. Cosmologically distributed gravitational microlenses could be localized in galaxies (or even in bulge or halo of gravitational macrolenses) or could be distributed in a uniform way. We have analyzed both cases of such distributions. We found that the optical depth for gravitational microlensing caused by cosmologically distributed deflectors could be significant and could reach $10^{-2} - 0.1$ at $z\sim 2$. This means that cosmologically distributed deflectors may contribute significantlly to the X-ray variability of high-redshifted QSOs ($z>2$). Considering that the upper limit of the optical depth ($\tau\sim 0.1$) corresponds to the case where dark matter forms cosmologically distributed deflectors, observations of the X-ray variations of unlensed QSOs can be used for the estimation of the dark matter fraction of microlenses.Comment: 6 pages, to appear in "Impact of Gravitational Lensing on Cosmology", IAU Symposium 225, eds. Y. Mellier & G. Meyla