Spherical Accretion in Alternative Theories of Gravity

The groundbreaking image of the black hole at the center of the M87 galaxy has raised questions at the intersection of observational astronomy and black hole physics. How well can the radius of a black hole shadow be measured, and can this measurement be used to distinguish general relativity from other theories of gravity? We explore these questions using a simple spherical flow model in general relativity, scalar Gauss-Bonnet gravity, and the Rezzolla and Zhidenko parameterized metric. We assume an optically thin plasma with power-law emissivity in radius. Along the way we present a generalized Bondi flow, as well as a piecewise analytic model for the brightness profile of a cold inflow. We use the second moment of a synthetic image as a proxy for EHT observables and compute the ratio of the second moment to the radius of the black hole shadow. We show that corrections to this ratio from modifications to general relativity are subdominant compared to corrections to the critical impact parameter, and we argue that this is generally true. In our simplified model the astrophysical parameter uncertainty dominates the gravity theory parameter uncertainty, underlining the importance of understanding the accretion model if EHT is to be used to successfully test theories of gravity.