Constraints on a charge in the Reissner--Nordstr\"om metric for the
  black hole at the Galactic Center
  Using an algebraic condition of vanishing discriminant for multiple roots of
fourth degree polynomials we derive an analytical expression of a shadow size
as a function of a charge in the Reissner -- Nordstr\"om (RN) metric
\cite{Reissner_16,Nordstrom_18}. We consider shadows for negative tidal charges
and charges corresponding to naked singularities $q=\mathcal{Q}^2/M^2 > 1$,
where $\mathcal{Q}$ and $M$ are black hole charge and mass, respectively, with
the derived expression. An introduction of a negative tidal charge $q$ can
describe black hole solutions in theories with extra dimensions, so following
the approach we consider an opportunity to extend RN metric to negative
$\mathcal{Q}^2$, while for the standard RN metric $\mathcal{Q}^2$ is always
non-negative. We found that for $q > 9/8$ black hole shadows disappear.
Significant tidal charges $q=-6.4$ (suggested by Bin-Nun (2010)) are not
consistent with observations of a minimal spot size at the Galactic Center
observed in mm-band, moreover, these observations demonstrate that a Reissner
-- Nordstr\"om black hole with a significant charge $q \approx 1$ provides a
better fit of recent observational data for the black hole at the Galactic
Center in comparison with the Schwarzschild black hole.
