SUPERMASSIVE BLACK HOLE AT THE GALACTIC CENTER

We derive an analytical expression of a shadow size as a function of a charge in the Reissner-Nordstrom (RN) metric. Using the derived expression we consider shadows for negative tidal charges and charges corresponding to naked singularities q=Q^2/M^2 > 1, where Q and M are black hole charge and mass, respectively. An introduction of a negative tidal charge q can describes black hole solutions in theories with extra dimensions, so following the approach we consider an opportunity to extend RN metric to negative Q^2, while for the standard RN metric Q^2 is always non-negative. We found that for q > 9/8 black hole shadows disappear. Significant tidal charges q=-6.4 are not consistent with observations of a minimal spot size at the Galactic Center observed in mm-band, moreover, these observations demonstrate that in comparison with the Schwarzschild black hole a Reissner-Nordstrom black hole with a significant charge q » 1 provides a better fit of recent observational data for the black hole at the Galactic Center