Quantum Effects of Black Holes

Abstract

We study quantum mechanical aspect of black holes. We give a brief re view of black hole radiation which is commonly called Hawking radiation. So far several different methods have been employed to investigate this radiation and all these results suggest in favor of the existence of Hawking radiation. However, there still exist several aspects of the Hawking effect which have yet to be clarified. We outline some arguments from previous works on the subject and then attempt to present the more satisfactory derivations of Hawking radiation by using semi-classical tunneling mech anism for nonrotating and rotating background spacetimes. We employ three kinds of methods for investigating the tunneling radiation: the null geodesic method, the Hamilton-Jacobi ansatz, and the Damour-Ruffini method. All these methods lead to the same conclusion. However, the Hamilton-Jacobi ansatz is more simple and the physical picture in this method is more clear. We also discuss thermodynamic properties like entropy of different black holes. We obtain inner horizon entropy and Bekenstein-Smarr Formula as well. In some recent derivations thermal characters of the inner horizon have been employed; however, the understanding of possible role that may play the inner horizons of black holes in black hole thermodynamics is still somewhat incomplete. Motivated by this problem we investigate Hawking v radiation of black holes by considering thermal characters of both the outer and inner horizons. We investigate Hawking radiation of electrically and magnetically charged Dirac particles (as well as scalar particles) from more general black hole spacetimes (such as Demia´nski-Newman and Kerr Newman-Kasuya-Taub-NUT-Anti-de Sitter black hole). Taking into account conservation of energy and the back-reaction of particles to the spacetime, we calculate the emission rate and find it pro portional to the change of Bekenstein-Hawking entropy. The radiation spectrum deviates from the precisely thermal one and the investigation specifies a quantum-corrected radiation temperature dependent on the black hole background and the radiation particle’s energy, angular mo mentum, and charges. It also has been found that Dirac particles are emitted at the same temperature as scalar particles from a black hole. It depicts the robustness of the semi-classical tunneling technique.