  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.
