Localization Of Elko Field On Brane World And Qusibound States Around Black Hole

The investigation of dark matter is one of the forefront of research. In the numerous candidates of dark matter, the Elko field possesses some properties which can describe well the dark matter. Thus it is regarded as one of the important candidates of dark matter.On the other hand, the brane worlds attract everyone’s attention by their ability to solve some of the great problems in physics, such as the hierarchy problem, and the cosmological constant problem. In the brane world theory, investigation about the lo-calization of the matter field on the brane is very important. By the localization of the matter field, we can reconstruct the standard model of the field theory on the brane and give the suggestion for our experiments in the future.At the same time, the matter like candidates of dark matter, such as the Elko, has the challenge from the "no hair" theory of black hole. The "no hair" theorem refuses that there exists stationary matter field around a black hole except the electromagncfic field. But this theorem does not refuse the matter field which evolves very long time around a black hole. Recently, some one introduced a new kind of matter field configuration which can stay for a long time around a black hole:quasibound state. Its life time may reach the age of the universe. This new kind of field configuration attracts people’s attention as soon as it appears.In this thesis, firstly we investigate the localization of the 5D free massless Elko spinors and the 5D Elko spinors with coupling term on Minkowski branes. We consider both the thin brane and the thich brane. We find that for the 5D free massless Elko field, the zero mode and massive KK modes all can not be localized on Minkowski branes, included both the thin brane and the thick brane. And for the 5D Elko spinors with coupling term, there will exist bound Elko zero mode in Randall-Sundrum brane model only if we introduce a negative 5D mass term. And when we introduce the Yukawa type coupling term, the Elko zero mode can be localized on some special thick branes with a particular coupling constant. Nevertheless, the massive KK modes still can not be localized on these branes. In addition, we simply consider the localization of the zero mode of the 5D free massless Elko spinors on the de Sitter/anti de Sitter thin brane. We find the zero mode still can not be localized on the de Sitter/anti de Sitter thin brane. There are many challenges in the localization of the Elko spinors and it needs us to introduce more brane world models and coupling ways.Secondly, we extend the research of the quasibound states of matter field from the scalar field around a Schwarzschild black one to the Dirac filed. We find, for the Dirac quasibound states around a Schwarzschild black hole, the lifetime of the Dirac quasibound states increases with the decrease of the mass of Dirac field, and increases with the addition of the total angular momentum, and depends on the spin-orbit interaction. In particular, for ultra-light Dirac field, the corresponding particles can stay around a Schwarzschild black hole for a very long time, even for cosmological time-scales.Finally, we investigate the scalar quasibound states around a Schwarzschild de-Sitter black hole, we find the number of resonance states is not unlimited any more and decreases with the additon of the cosmological constant. At the same time, a new kind of resonance which we call as "top resonance" is found. The top resonance is very different from the normal resonance and there exists not obvious "main peak" in the shape of its solution. The result of evolution shows that for the normal scalar quasibound states, the lifetime will decrease with the increase of the mass of scalar field, and the top one can not stay for a very long time as the other normal resonance. shows an exponential decay, but for the top one, the energy will fall quickly. The decay rate of energy depends on the resonant frequency, the mass of scalar filed and the cosmological constant. In particular, for the meaningful cosmological constant in cosmology and for ultra-light scalar field, the life time corresponding particles will be very long, even for cosmological time-scales.