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.