Black Hole Entropy, Black Hole Information Paradox & Quantum Teleportation In Curved Space-time

The origins of black hole entropy and the black hole information paradox have long been puzzled problems to most theoretical physicists. This thesis is devoted to investigating black hole entropy by using the membrane method, and trying to find a possible way of solving the black hole information problem. Moreover, we demonstrate how black holes can influence the fidelity of quantum teleporation. And then we show sonic black holes might be useful in quantum teleporation. At the end of the paper, we discuss the possibility of using black holes as quantum computers.The thesis consists of five parts. The first part is the introduction; the second part is about the origins of black hole entropy; the third part is about the black hole information paradox, which also includes the relations between the black hole complementarity and quantum non-cloning theorem; the fouth part is about quantum teleporation in the background of curved space-time and a theoretical model of black hole computers. The last part present the conclusions.In the second chapter, using the approved brick wall method, we studied the quantum entropy of various black holes, especially a class of black hole whose Euler characteristics is over 2. We is to show the formula S = (1/8)XA has its limitations: the equation does not apply to high dimensional black holes (X(s^2k+1) = 0), even does not apply to four dimensional black holes. Black hole entropy in string theory is also briefly discussed.In third chapter, We extend Horowitz and Maldacena's proposal about black hole final state to Dirac fields and find that if annihilation of the infalling positrons and the collapsed electrons inside the horizon is considered, then the nonlinear evolution of collapsing quantum state will be avoided. We further propose that annihilation also plays the central role in the process of black hole information escaping in both Dirac and scalar fields. The computation speed of a black hole is briefly discussed. Then, quantum non-cloning theorem and a thought experiment are discussed for charged black holes whose global struc-...