The Event Horizon Telescope is a millimeter VLBI array that aims to take the first pictures of the black holes in the center of the Milky Way and of the M87 galaxy, with horizon scale resolution. Measurements of the shape and size of the shadows cast by the black holes on the surrounding emission can test the cosmic censorship conjecture and the no-hair theorem and may find evidence for classical effects of the quantum structure of black holes. Observations of coherent structures in the accretion flows may lead to accurate measurements of the spins of the black holes and of other properties of their spacetimes. For Sgr A*, the black hole in the center of the Milky Way, measurements of the precession of stellar orbits and timing monitoring of orbiting pulsars offer complementary avenues to the gravitational tests with the Event Horizon Telescope.
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