Black Hole Entropy, The Black Hole De Broglie-bohm, Quantization, And Quintessence Cosmology,

The thesis consistes of four parts. The first part is about the quantum statistical entropy of black holes, the second part is about the canonical quantization of black holes and its de Broglie-Bohm interpretation, the third part is about the quintessence universe and the fourth part is about the classical and quantum wormholes with tachyon field. So, the whole paper is divided into four chapters. In the first chapter, using the thermal atmosphere method proposed by t 'Hooft, we studied the quantum statistical entropy of various black holes(static,stationary and low and high dimensions). We investigated the entropy of general static and spherical black holes due to arbitrary spin fields and presented the direct proportion relation between the entropy and the field degeneracy. The entropy of stationary and rotating black holes due to massed and charged scalar field and Dirac field is obtained. It shows that black holes entropy is not related to the mass and charge of the field particles. Furthermore we proposed not to consider the entropy contribution of non-thermal radiation here. The entropy of low dimensional black holes duo to scalar and Dirac field is also obtained. Compared with that of four-dimensional case, it reveals that the ratio of Dirac filed entropy to scalar field entropy is closely related to the dimension of space-time. The entropy of high dimensional black holes due to scalar and Dirac field is lastly obtained. It shows that the black holes entropy, whether due to scalar field or due to Dirac field, it always depends on the dimension of P-brane. The ratio of Dirac part to scalar part is also related to the space-time dimensions. In the second chapter, we made canonical quantization and de Broglie-Bohm interpretation on two kinds of black holes. By quantizing the two kinds of space-time which has the torus-like topology or has a monopole or cosmic string, we obtained the solutions of their Wheeler-De Witt equation. The solutions can both be expressed as the zero order and second kind Hankel function. Applying de Broglie-Bohm interpretation on the wave function, we got the quantum form of two kinds of space-time. In the end, the thermal effect of classical and quantum black holes is discussed. We pointed out that in order to avoid the divergence of Hawking temperature, we should introduce a cut-off with the order of Plank scale in the vicinity of event horizon. In the third chapter, we discussed the probability of non-minimally coupled complex scalar field as the cosmos dark energy-quintessence and presented an eternal expanding universe driven by real scalar field. The discussion of Kasuya shows that the minimally coupled complex scalar field is unstable to play the role of dark energy in the background of universe. So we discussed the non-minimally coupled case. We verified that the non-minimally coupled complex scalar field is stable undercertain condition and can play the role of dark energy. Its contribution to universe energy density comes from two forms. One is from the rotating effect of field and the other is from the coupled effect of field and gravity. Both of these effects are remarkably important in the evolution of universe. On the other hand, the observations of supernovae Ia by astronomers reveal that ever since the universe was created it has undergone a decelerating-accelerating epoch. Whereas we presented a toy model of eternal expanding universe which has an endless sequence of accelerating-decelerating cycles. In the fourth chapter, we discussed the classical and quantum wormholes with tachyon field. Recently Sen's remarkable work enables our research of tachyon field to make great progress. We discussed the classical and quantum wormholes with tachyon field. Starting from the general Lagrangian of tachyon, we deduced the wormhole equation, which has the topology of R 1 ? S3. Without the knowledge of coefficient ωfor state equation, we presented the classical and quantum wormhole solution in sections by specializing at some probable values of ω.