Fermion’s Tunnelling From Black Holes With Quantum Gravity Correction

Almost every quantum gravity theory predict the existence of a minimum measurable length. Black hole is a perfect system to investigate quantum gravity theory. Utilized the quantum field theory of curved space-time, the conclusion that black hole exist pure thermal spectrum radiation had been proved by Hawking. Though Per Kraus, Frank Wilczek and Maulik K.Parikh et al had proposed the tunnelling method of Hawking radiation and obtained beautiful correction result, the effect of minimum measurable length had not been considered.At present, some work about black hole’s radiation has been done with considering the quantum gravity influence. This is profound to investigate whether existing evapo-ration remnant and the information loss difficult. By employing a new quantum gravity correction method and Hamilton-Jacobi method of Tunnelling with semi-classical approx-imation, we have investigated the fermions tunnelling under the effect of quantum gravity and gained meaningful result.In Chapter 1, we introduce the background knowledge of black hole and Hawking radiation. Among them, we underline the tunnelling idea of Hawking radiation and its Geodesic method and Hamilton-Jacobi method.In Chapter 2, we introduce the minimum measurable length of quantum gravity and propose a new correction method of quantum gravity. The existence of a minimum measurable length has been predicted by almost every quantum gravity theory. One effective way to bring the minimum measurable length in mathematical theory is by means of generalized uncertainty principle(GUP). We propose a more reasonable and effective revised method.In Chapter 3, by employing semi-classical Hamilton-Jacobi method and the new method of quantum gravity correction proposed by us, we investigate the fermions tun- nelling problem through event horizon of Schwarzschild black hole, Reissner-Nordstrom black hole, Kerr black hole and Kerr-Newman de Sitter black hole one by one. The result of front three black hole imply that the quantum gravity effect not only make the radiation spectrum departed from pure thermal spectrum, but also retard the black hole’s evapo-ration and may lead to remnant. By investigating the Kerr-Newman de Sitter black hole, we recover the front results exactly and gain the corrected result of Kerr-Newman black hole directly. For the convenience of calculation and in order to observe the influence of quantum gravity, we ignore the back reaction of the radiating particle.In Chapter 4, we make a summary and outlook of this paper.