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 – Nordström (RN) metric. Using the derived expression we consider shadows for negative tidal charges and charges corresponding to naked singularities q = Q/M > 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, while for the standard RN metric Q 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 – Nordström black hole with a significant charge q ≈ 1 provides a better fit of recent observational data for the black hole at the Galactic Center.