paper

Constraints on a charge in the Reissner--Nordström metric for the black hole at the Galactic Center

arXiv:1407.7457 · doi:10.1103/PhysRevD.90.062007

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 \cite{Reissner_16,Nordstrom_18}. 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 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 (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 -- 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.

18 pages, 1 figure, accepted for publication in Physical Review D. arXiv admin note: text overlap with arXiv:astro-ph/0505286, arXiv:1407.2591. substantial text overlap with arXiv:1407.2591

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