These are exciting times for people interested in the observable
counterparts of strong gravity. Besides the new window recently
opened by gravitational-wave astronomy, the more classical
electromagnetic astronomy might also allow us in the close
future to probe strong gravity in a regime that was not accessible before.

The Event Horizon Telescope is a network of millimetric antennas
that aims at imaging the shadow of the supermassive black hole
Sgr A* at the center of the Galaxy, i.e. the dark patch on sky
due to the radiation that is swallowed by the hole. The ultimate
goal of the instrument is, by demonstrating the presence of this
shadow, to give the most convincing proof that Sgr A* is indeed
a black hole.

In this talk, I will investigate two questions related to this
general context : (1) does the detection of a shadow indeed
allows us to conclude that there is a black hole at the Galactic center ?
(2) would a black hole different from the standard Kerr solution
lead to a different shadow, in a way that could be detectable ?