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Recent images from the Event Horizon Telescope of accreting supermassiveblack holes (BHs), along with upcoming observations with better sensitivity andangular resolution, offer exciting opportunities to deepen our understanding ofspacetime in strong gravitational fields. A significant focus for future BHimaging observations is the direct detection of the "photon ring," a narrowband on the observer's sky that collects extremely lensed photons. The photonring consists of self-similarly nested subrings which, in spherically-symmetricspacetimes, are neatly indexed by the maximum number of half-loops executedaround the BH by the photons that arrive in them. Each subring represents anentire "higher-order" image of the horizon-scale accretion flow. Furthermore,this self-similarity is controlled by a single critical lensing exponent linkedto the radial (in)stability of photon orbits near the critical (circular)photon orbit, solely determined by the spacetime geometry. However, extractingsuch information about the spacetime geometry can be challenging because theobserved photon ring is also influenced by the structure of the emittingregion. To address this, we conducted a comprehensive study by varying (a) awide range of emission-zone morphology models and (b) families of spacetimemetrics. We find that the lensing exponent can be reliably determined fromfuture observations. This exponent can provide access to the $rr-$component ofthe spacetime metric, as well as significantly narrow down currently accessibleBH parameter spaces. Additionally, the width of the first-order photon subringserves as yet another important discriminator of the spacetime geometry.Finally, observations of flaring events across different wavelengths mightreveal time-delayed secondary images, with the delay time providing a promisingnew way to independently estimate the BH shadow size.

Extreme Light Bending in Spherically-Symmetric Black Hole Spacetimes: Universal Characteristics and Strong-Field Tests of Gravity