Entropy spectrum and area spectrum of a modified Schwarzschild black hole via an action invariance

The spectroscopy of a quantum corrected Schwarzschild black hole in the gravity's rainbow is investigated. By utilizing an action invariance of the black hole and with the help of Bohr–Sommerfield quantization rule, the entropy and area spectrum for the modified black hole are calculated. Here, the quasinormal modes of the black hole is not used. The obtained entropy spectrum is equally spaced and has not dependence on the quantum effects of the spacetime. However, due to the spectime quantum effects of the modified black hole, the obtained area spectra is not equally spaced and the area spacing depend on the horizon area of the black hole. But, as the same to the entropy spectrum, the area spectrum of the gravity's rainbow is independent of the energy of test particle, although the modified spacetime has the dependence on the particle energy.