  An active stage of relativistic astrophysics started in 1963 since in this
year, quasars were discovered, Kerr solution has been found and the first Texas
Symposium on Relativistic Astrophysics was organized in Dallas. Five years
later, in 1967--1968 pulsars were discovered and their model as rotating
neutron stars has been proposed, meanwhile J. A. Wheeler claimed that Kerr and
Schwarzschild vacuum solutions of Einstein equations provide an efficient
approach for astronomical objects with different masses. Wheeler suggested to
call these objects black holes. Neutron stars were observed in different
spectral band of electromagnetic radiation. In addition, a neutrino signal has
been found for SN1987A. Therefore, multi-messenger astronomy demonstrated its
efficiency for decades even before observations of the first gravitational
radiation sources. However, usually, one has only manifestations of black holes
in a weak gravitational field limit and sometimes a model with a black hole
could be substituted with an alternative approach which very often looks much
less natural, however, it is necessary to find observational evidences to
reject such an alternative model. After two observational runs the LIGO-- Virgo
collaboration provided a confirmation for an presence of mergers for ten binary
black holes and one binary neutron star system where gravitational wave signals
were found. In addition, in last years a remarkable progress has been reached
in a development of observational facilities to investigate a gravitational
potential, for instance, a number of telescopes operating in the Event Horizon
Telescope network is increasing and accuracy of a shadow reconstruction near
the Galactic Center is improving, meanwhile largest VLT, Keck telescopes with
adaptive optics and especially, GRAVITY facilities observe bright IR stars at
the Galactic Center with a perfecting accuracy.
