Hawking radiation and black hole entropy in a gravity's rainbow

In the context of gravity's rainbow, Planck scale correction on Hawking radiation and black hole entropy in Parikh and Wilczk's tunneling framework is studied. We calculate the tunneling probability of massless particles in the modified Schwarzschild black holes from gravity's rainbow. In the tunneling process, when a particle gets across the horizon, the metric fluctuation must be taken into account, not only due to energy conservation but also to spacetime Planck scale effect. Our results show that the emission rate is related to changes of the black hole's quantum corrected entropies before and after the emission. In the same time, for the modified black holes, a series of correction terms including a logarithmic term to Bekenstein-Hawking entropy are obtained. Correspondingly, the spectrum of Planck scale corrected emission is obtained and it deviates from the thermal spectrum. In addition, a specific form of modified dispersion relation is proposed and applied.