Qualitative Shadow Anomaly as a Smoking-gun Signature of Nonmetricity

Abstract

In general relativity and its metric-formalism extensions, the innermost stable circular orbit and the photon ring of a charged black hole contract as the charge increases. In this paper, we discover a qualitative anomaly that violates this universal behavior, serving as a smoking-gun signature of geometric nonmetricity. By considering a minimal coupling between the bosonic field and the independent affine metric, we demonstrate that nonmetricity induces an effective geometric force that triggers a trajectory expansion of both massless and massive bosons with increasing black hole charge. This qualitative inversion directly imprints onto the black hole shadow, lifting the degeneracy between metric-affine gravity and general relativity. Using Eddington-inspired Born-Infeld gravity as a concrete implementation, we show that next-generation horizon-scale imaging can resolve this signature, probing a complementary high-energy window up to the $10^{5}_{~}\,\text{TeV}$ scale.