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

Abstract

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.

Remnants of black rings from gravity’s rainbow

“…This choice is supposed to be based on phenomenological motivations. Among different arbitrary choices in [17][18][19][20][21][22][23][24], many aspects of the theory have been studied with FRW universe and black hole thermodynamics. Among the proposals in the literature, we use one of the most interesting and the most studied modified dispersion relations that was proposed by Amelino-Camelia, et al in [1,2] f (E/E P ) = 1,…”

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

“…Then, from (43) and (47), it is implied that, information conservation of black hole is still possible when the quantum corrections of black hole entropy are considered. In addition, the corrected item S QC of the black hole entropy can be calculated by giving the specific form of the energy function f [39,40,62,68]. Then, from (43), the radiation spectrum with quantum corrections and the information deposited by the spectrum can be investigated further.…”

“…Thence, by the Hamilton-Jacobi method, the quantum correction to the tunneling program was discussed and the quantum corrected entropy of black holes was calculated [26][27][28][29][30][31][32][33]. Also, in the radial trajectory method, the quantum effects of spacetime was considered and the emission rate was related the quantum corrected entropy of black hole [34][35][36][37][38][39][40][41][42][43]. These results show that, considering the quantum corrections of black hole entropy and spacetime, information conservation of black hole is still possible.…”

“…The modified Schwarzschild solution in gravity's rainbow has been given [57]. Further, the thermodynamics [39,40,[62][63][64] and geometry structure [65][66][67] of the modified Schwarzschild black hole have been investigated.…”

Quantum Corrections for a Bardeen Regular Black Hole

“…Srinivasan and Padmanabhan [6] introduced another technique based on the Hamilton-Jacobi method. Planck's scale correction in the Parikh-Wilczek tunneling framework was studied by many people [8][9][10]. Jiang et al [8] investigated Hawking radiation as massless charged particles tunneling across the event horizon of Kerr and Kerr-Newmann BHs.…”