A test of Einstein's equivalence principle in future VLBI observations

We show that very-long-baseline-interferometry (VLBI) observations of supermassive black holes will allow us to test the fundamental principles of General Relativity (GR). GR is based on the universality of gravity and Einstein's equivalence principle (EEP). However, EEP is not a basic principle of physics but an empirical fact. Non-minimal coupling (NMC) of electromagnetic fields violates EEP, and their effects manifest in the strong-gravity regime. Hence, VLBI observations of black holes provide an opportunity to test NMC in the strong-gravity regime. To the leading order in the spin parameter, we explicitly show that the NMC of the electromagnetic field introduces observable modifications to the black hole image. In addition, we find that the size of the photon rings varies by $\sim 3 r_H$, which corresponds to $\sim 30 \mu as$ for Sagittarius $A^*$ and $\sim 23 \mu as$ for M87. VLBI telescopes are expected to attain a resolution of $\sim 5 \mu as$ in the near future. However, direct detection of photon ring will require the resolution of $\sim 1 \mu as$ for M87, which can potentially be probed by the space-based Event Horizon Explorer.