Photon rings of spherically symmetric black holes and robust tests of non-Kerr metrics

Under very general assumptions on the accretion flow geometry, images of a black hole illuminated by electromagnetic radiation display a sequence of photon rings (demagnified and rotated copies of the direct image) which asymptotically approach a purely theoretical critical curve - the outline of the black hole photon shell. To a distant observer, these images appear dominated by the direct emission, which forms a ring whose diameter is primarily determined by the effective radius of the emitting region. For that reason, connecting the image diameter seen by a distant observer to the properties of the underlying spacetime crucially relies on a calibration that necessarily depends on the assumed astrophysical source model. On the other hand, the diameter of the photon rings depends more on the detailed geometry of the spacetime than on the source structure. As such, a photon ring detection would allow for the spacetime metric to be probed in a less model-dependent way, enabling more robust tests of General Relativity (GR) and the Kerr hypothesis. Here we present the photon ring structure of several spherically symmetric black hole spacetimes and perform comparisons with the Schwarzschild/Kerr case. We offer our perspective on future tests of the spacetime metric with photon rings, discussing challenges and opportunities involved.