About Some Of The Black Hole Entropy And Through The Wormhole

There are four chapters in this doctor thesis.In chapter 1-we introduce the knowledge and recent development of black hole thermodynamics and traversable wormhole.In chapter 2-The brick-wall method based on the thermal equilibrium in large scale can't be applied to the cases of non-equilibrium, such as the non-stationary space-time with two horizons, for example, Vaidya-de Sitter space-time. We improve the brick-wall method and propose the thin-layer method. The entropies of scalar and spinor fields in Vaidya-de Sitter space-time are calculated by the thin-layer method. The condition of local equilibrium near the two horizons is used as a working postulate and it is maintained for the black hole which evaporates enough slowly and whose mass is far greater than the Planck mass. There are two horizons in Vaidya-de Sitter space-time. We think that the total entropy is mainly attributed to the two layers near the two horizons. The entropy of scalar field in Vaidya-de Sitter space-time is linear sum of the area of black hole horizon and that of cosmological horizon. Thinking of Dirac equations in Newman-Penrose formalism, there are four components of the wave function F1,F2, G1 and G2. The total entropy is summed up from the entropies corresponding to the four components. On the same condition of scalar field, the resulting entropy is 7/2 times that of scalar field, and is also linear sum of the area of black hole horizon and that of cosmological horizon. The difference from the stationary black hole is that the result relies on time-dependent cutoffs.