Constraints on a Tidal Charge of the Supermassive Black Hole in M87* with the EHT Observations in April 2017

Alexander Zakharov

doi:10.3390/universe8030141

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–Nordström metric have been obtained. Some time ago, Bin-Nun proposed to apply a Reissner–Nordström metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr A*. If we assume that a Reissner–Nordström 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*.

Highlights

The Very Long Baseline Interferometry (VLBI) technique for observations of compact bright radio sources has been proposed in Union of Soviet Socialist Republics in sixties of the last century and these ideas were realized in the joint experiment United States– Russian experiment proposed by M
In 2004–2005 we knew that scattering may spoil a shadow image at 1.3 cm as it was shown in [14–16]2 and 1.3 mm is a more suitable wavelength for a shadow detection as we noted in [7], we promoted an opportunity to detect the Sgr A* shadow with VLBI acting in mm and sub-mm bands, in particular, we discussed an opportunity to use the ground–space interferometer Millimetron facilities for observations of bright structures around the shadow for its reconstruction in Sgr A* (in these years we did not know about the Event Horizon Telescope (EHT) project)
If in future a shadow size estimate will be significantly larger than it is expected in the Schwarzschild black hole case we will conclude that the Reissner-Nordström metric with a tidal charge might be considered as a more suitable model instead of the Schwarzschild black hole

Summary

Introduction

The Very Long Baseline Interferometry (VLBI) technique for observations of compact bright radio sources has been proposed in Union of Soviet Socialist Republics in sixties of the last century and these ideas were realized in the joint experiment United States– Russian experiment proposed by M. Hordeski in [27] and these studies were forgotten for several years but a number of applications of Horndeski theories (and their generalizations) have been considered in last years (see, for instance [28]) As it was shown in [29] in the framework of the Horndeski approach for scalar-tensor theories a black hole could have a secondary hair q due to the non-trivial scalar-tensor mixing and the corresponding solution looks like a Reissner–Nordström metric with a non-electric charge. Relativistic precession for such Reissner–Nordström black holes with a tidal charge are evaluated in [30] (it gives an opportunity to constrain a black hole charge from Very Large Telescope and Keck observations of bright stars moving near the Galactic Center).

Motivation

An Analytical Expression for Shadow Radius as a Function of Charge

Constraints from Observations of Sgr A*

Discussion

Conclusions