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

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 q = Q 2 /M 2 > 1, where 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 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 (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 q ≈ 1 provides a better fit of recent observational data for the black hole at the Galactic Center in comparison with the Schwarzschild black hole.

The Milky Way’s Supermassive Black Hole: How Good a Case Is It?

“…As the electrical force field is about 40 magnitudes larger than the gravitational field, it is thought to be unlikely that significant netto charges can be accumulated with black holes. There is the possibility that the black hole shadow disappears if an appreciable charge is accumulated (Zakharov, 2014). However, the shadow of a black hole is not a very clean observable, and inclinations and accretion phenomena may cause the disappearance (or washiness) of a shadow as well.…”

Graviton mass evaluation with trajectories of bright stars at the Galactic Center

“…spectral line structure [1,2,3] 8 (see also more recent reviews [11,12] on the subject). Another phenomenon, where one really needs a strong gravitational field approach, is simulations of a shadow formation started since [13,14,15,16] (see also calculations of shadows for different cases [17,18,19,20,21,22] and recent reviews on the subject [23,24]). The problem is connected with attempts to resolve the smallest spot at the Galactic Center with VLBI interferometry in mm-band [25].…”

Shadow size for the supermassive black hole at the Galactic Center

“…One can find a more detailed description of our results in papers 15,21,22,[29][30][31][32][33][34][35] .…”

“…Therefore, a probability to have so significant tidal charge for the black hole at the Galactic Center is negligible. So, we could claim that the tidal charge is ruled out with observations and corresponding theoretical analysis [20][21][22][23][24][25] . In Fig.…”