**Publication date:** Jul 2018

**Abstract:**

The classical general relativity (GR) is remarkably confirmed in different astronomical tests. Recently, gravitational waves have been detected from binary black holes and binary neutron starsystems. Moreover, constraints on alternative theories of gravity have been obtained, so thatgraviton mass bounds have been found such as m_g < 7.7 × 10^{-23} eV. It means that theories of massive gravity,if they are realized in nature, have to be very close to GR.In spite of a great progress of GR now there exist a number of alternative theories of gravity,such as f(R) theories, theories of massive gravity, scalar-tensor theories etc.Scalar-tensor theories proposed by Hordeski are among popular alternatives for classical general relativity (GR).There are no-hair theorems in such a theory, however, there exist hairy black hole solutions under some assumptions.for instantce, Babichev et al. (2017) constructed a set of hairy static black hole solutions (for quarticHordeski Lagrangian of scalar-tensor theory of gravity). We show that analytical expressions for shadow sizeobtained for Reissner - Nordström metric (with electric and tidal charges) may be usedto compare theoretical predictions and observations for asymptotically flat black holes with a scalar hair which mimics an electric charge.We present analytical expressions for shadow size for static black hole solutions with de-Sitter and anti-de-Sitter asymptotics.The relations could be used for comparison of the theoretical models with observational data obtained with the Event Horizon Telescope for the black hole at the Galactic Center or in galaxy M87.
**Authors:**

Zakharov, Alexander; Stuchlik, Zdenek; Jaluvkova, Pavlina; Tursunov, Arman;