Abstract
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-Nordström (RN) metric [1,2]. We consider shadows for negative tidal charges and charges corresponding to naked singularities , where and are black hole charge and mass, respectively, with the derived expression. An introduction of a negative tidal charge can describe black hole solutions in theories with extra dimensions, so following the approach we consider an opportunity to extend the RN metric to negative , while for the standard RN metric is always non-negative. We found that for , black hole shadows disappear. Significant tidal charges (suggested by Bin-Nun [3–5]) 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-Nordström black hole with a significant charge provides a better fit of recent observational data for the black hole at the Galactic Center in comparison with the Schwarzschild black hole.
- Received 5 March 2013
DOI:https://doi.org/10.1103/PhysRevD.90.062007
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