  To see how the gravity's rainbow works for black hole complementary, we
evaluate the required energy for duplication of information in the context of
black hole complementarity by calculating the critical value of the rainbow
parameter in the certain class of the rainbow Schwarzschild black hole. The
resultant energy can be written as the well-defined limit for the vanishing
rainbow parameter which characterizes the deformation of the relativistic
dispersion relation in the freely falling frame. It shows that the duplication
of information in quantum mechanics could not be allowed below a certain
critical value of the rainbow parameter; however, it might be possible above
the critical value of the rainbow parameter, so that the consistent formulation
in our model requires additional constraints or any other resolutions for the
latter case.
