The sign of the Herrera complexity factor at a light ring indicates whether that ring is a stable or unstable photon sphere, and zero-complexity compact objects cannot host external photon spheres.
This effective potential is used to determine the radius at which photon sphere might exist for the gravitating object
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Herrera Complexity and Shadows of Spherically Symmetric Compact Objects
The sign of the Herrera complexity factor at a light ring indicates whether that ring is a stable or unstable photon sphere, and zero-complexity compact objects cannot host external photon spheres.