**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;