  Rainbow gravity modifies general relativity by introducing an energy
dependent metric, which is expected to have a role in the quantum theory of
black holes and in quantum gravity at Planck energy scale. We show that rainbow
gravity can be simulated in the laboratory by nonlinear waves in nonlocal
media, as those occurring in Bose-condensed gases and nonlinear optics. We
reveal that at a classical level, a nonlocal nonlinear Schr\"odinger equation
may emulate the curved space time in proximity of a rotating black hole as
dictated by the rainbow gravity scenario. We also demonstrate that a fully
quantized analysis is possible. By the positive $\mathcal{P}$-representation,
we study superradiance and show that the instability of a black-hole and the
existence of an event horizon are inhibited by an energy dependent metric. Our
results open the way to a number of fascinating experimental tests of quantum
gravity theories and quantum field theory in curved manifolds, and also
demonstrate that these theories may be novel tools for open problems in
nonlinear quantum physics.
