  We study the equivalence principle, regarded as the cornerstone of general
relativity, by analyzing the deformation observable of black hole shadows. Such
deformation can arise from new physics and may be expressed as a
phenomenological violation of the equivalence principle. Specifically, we
assume that there is an additional background vector field that couples to the
photons around the supermassive black hole. This type of coupling yields impact
on the way the system depends on initial conditions, and affects the black hole
shadow at different wavelengths by a different amount, and therefore
observations of the shadow in different wavelengths could constrain such
couplings. This can be tested by future multi-band observations. Adopting a
specific form of the vector field, we obtain constraints on model parameters
from Event Horizon Telescope observations and measurements of gas/stellar
orbits.
