Abstract. The standard Hawking formula predicts the complete evaporation of black holes.In this paper, we introduce effects of quantum gravity into fermions' tunneling from ReissnerNordstrom and Kerr black holes. The quantum gravity effects slow down the increase of Hawking temperatures. This property naturally leads to a residue mass in black hole evaporation. The corrected temperatures are affected by the quantum numbers of emitted fermions. Meanwhile, the temperature of the Kerr black hole is a function of θ due to the rotation.arXiv:1307.0172v2 [gr-qc]

Hawking radiation from black hole horizon can be viewed as a quantum tunnelling process, and fermions via tunnelling can successfully recover Hawking temperature. In this paper, considering the tunnelling particles with spin 1/2 (namely, Dirac particles), we further improve Kerner and Man's fermion tunnelling method to study Hawking radiation via tunnelling from rotating black holes in de Sitter spaces, specifically including that from Kerr de Sitter black hole and Kerr-Newman de Sitter black hole. As a result, Hawking temperatures at the event horizon (EH) and the cosmological horizon (CH) are well described via Dirac particles tunnelling.

In this review, we discuss effects of quantum gravity on black hole physics. After a brief review of the origin of the minimal observable length from various quantum gravity theories, we present the tunneling method. To incorporate quantum gravity effects, we modify the Klein-Gordon equation and Dirac equation by the modified fundamental commutation relations. Then we use the modified equations to discuss the tunneling radiation of scalar particles and fermions. The corrected Hawking temperatures are related to the quantum numbers of the emitted particles. Quantum gravity corrections slow down the increase of the temperatures. The remnants are observed as M Res. The mass is quantized by the modified Wheeler-DeWitt equation and is proportional to n in quantum gravity regime. The thermodynamical property of the black hole is studied by the influence of quantum gravity effects.

Kerner and Mann's recent work shows that, for an uncharged and non-rotating black hole, its Hawking temperature can be correctly derived by fermions tunnelling from its horizons. In this paper, our main work is to improve the analysis to deal with charged fermion tunnelling from the general dilatonic black holes, specifically including the charged, spherically symmetric dilatonic black hole, the rotating Einstein-Maxwell-Dilaton-Axion (EMDA) black hole and the rotating Kaluza-Klein (KK) black hole. As a result, the correct Hawking temperatures are well recovered by charged fermions tunnelling from these black holes.