Black Hole Images as Tests of General Relativity: Effects of Plasma
  Physics
  The horizon-scale images of black holes obtained with the Event Horizon
Telescope have provided new probes of their metrics and tests of General
Relativity. The images are characterized by a bright, near circular ring from
the gravitationally lensed emission from the hot plasma and a deep central
depression cast by the black hole. The metric tests rely on fact that the
bright ring closely traces the boundary of the black hole shadow with a small
displacement that has been quantified using simulations. In this paper we
develop a self-consistent covariant analytic model of the accretion flow that
spans a broad range of plasma conditions and black-hole properties to explore
the general validity of this result. We show that, for any physical model of
the accretion flow, the ring always encompasses the outline of the shadow and
is not displaced by it by more than half the ring width. This result is a
consequence of conservation laws and basic thermodynamic considerations and
does not depend on the microphysics of the plasma or the details of the
numerical simulations. We also present a quantitative measurement of the bias
between the bright ring and the shadow radius based on the analytical models.
