Testing General Relativity with the Shadow Size of Sgr A*
  In general relativity, the angular radius of the shadow of a black hole is
primarily determined by its mass-to-distance ratio and depends only weakly on
its spin and inclination. If general relativity is violated, however, the
shadow size may also depend strongly on parametric deviations from the Kerr
metric. Based on a reconstructed image of Sagittarius A* (Sgr A*) from a
simulated one-day observing run of a seven-station Event Horizon Telescope
(EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that
such an observation can measure the angular radius of the shadow of Sgr A* with
an uncertainty of ~1.5 uas (6%). We show that existing mass and distance
measurements can be improved significantly when combined with upcoming EHT
measurements of the shadow size and that tight constraints on potential
deviations from the Kerr metric can be obtained.
