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When adopted in black hole spacetimes, geometric-optics approximations implya mapping between the quasinormal mode (QNM) spectrum of black holes in theeikonal limit and black hole images. In particular, the real part and theimaginary part of eikonal QNM frequencies are associated with the apparent sizeand the detailed structure of the ring images, respectively. Thiscorrespondence could be violated when going beyond general relativity. Wepropose a novel method to test the eikonal correspondence via the comparison oftwo sets of observables from a nonrotating black hole, one extracted from QNMspectra and the other from the lensed photon rings on the image plane.Specifically, the photon ring observables robustly capture the information ofthe black hole spacetime itself regardless of the surrounding emission models.Therefore, the proposed test of eikonal correspondence can be validated inquite broad scenarios.

A novel test of gravity via black hole eikonal correspondence