Spectroscopy of a charged black hole in gravity’s rainbow via an action invariance

The spectroscopy of a modified Reissner-Nordstrom black hole in gravity’s rainbow was 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 quantum corrected charged black hole were calculated. The equally spaced entropy spectrum being consistent to the original Bekenstein’s spectrum was derived. However, due to the spacetime quantum effect of the gravity’s rainbow, the obtained area spectra was not equally spaced and the area spacing depend on the horizon area. And that, the quantum corrections of the area spectrum and the black hole entropy to the original Bekenstein’s results were discussed. Besides, it was found that, the entropy and area spectrum of the modified charged black hole were independent of the energy of the test particle, although the modified spacetime itself has the energy dependence.