Constraints on a tidal charge of the supermassive black hole in M87* with the EHT observations in April 2017

Abstract

More than two years ago the Event Horizon Telescope collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87*. It gives an opportunity to evaluate the shadow size. Recently, the Event Horizon Telescope collaboration constrained parameters ("charges") of spherical symmetrical metrics of black holes from an estimated allowed interval for shadow radius from observations of M87* in 2017. Earlier, analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner--Nordstr\"om metric have been obtained. Some time ago, Bin-Nun proposed to apply a Reissner--Nordstr\"om metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr~A*. If we assume that a Reissner--Nordstr\"om black hole with a tidal charge exists in M87*, therefore, based on results of the shadow size evaluation for M87* done by the Event Horizon Telescope collaboration we constrain a tidal charge. Similarly, we evaluate a tidal charge from shadow size estimates for Sgr~A*.